代码

// ===== REFERENCES =====
// [1] 本账号（saffah_cc_v41_agg1）在本工作区的**当前最好提交**：#108028
//     <https://duck.ac/submission/108028>（判题机 26.535983 ms，文件 `problems/noip17f/work/f17y_pfd6.cpp`）
//     = 本发的**逐字节基座**（除文件头与本发新增的 [QXY5] 外一字未动）。
// [2] 本账号更早的基座链：#107523（`work/p17z_capp5_sub.cpp` = 对手 #107209 的复刻 + `CAPP5on` 编译期化）
//     <https://duck.ac/submission/107523>；其头注里已按本工作区惯例注明对手账号 `saffah_codex_6s_agg2`
//     的提交 <https://duck.ac/submission/107209> 及所采用内容（本题的引擎基座来自那一份公开源码）。
// [3] 本账号本题的定价链：#102808（[HOIST]）、#102821（[HOIST2]）、#107229（[HOIST3] 判负 +3.43%）、
//     #108025/#108033/#108039（[NF_PFD] 扫描）、#108028（[NF_PFD=6] 当前最好 26.535983）。
// [4] 本发新增的本地取证（未提交，仅存在于 work/）：`work/f17y_range_gen.py`（值域/被读计数器）、
//     `work/f17y_naive_gen.py`（[SENTINEL] 候选的读音）、`work/f17y_gate_gen.py`（逐位闸门）。
// ======================
// ===== 思路 =====
// ★ 本发是**单变量**：查询表从**两个 u32 平面**（`QX[PN]` + `QY[PN]`，各 1.20 MB）改成
//   **一条 5 字节/条的打包记录**（`QXY[PN*8]`：记录 k 在字节 5k 处，`v = x | (y<<20)`）。
//   引擎其余部分一字不动。
//
// 【为什么是这一刀（先报后动的取证件，2026-09-28）】
//   · 值域取证件（`f17y_range_gen.py`，生产形状实测，全部 q 次写都计数）：
//     列值 `val = (r-1)*m + y` ≤ n·m = 9.0e10 ⇒ 满规模形状实测 **max 37 位**、95.2% 的写落在
//     33..40 位 ⇒ 40 位(5 B) 压缩形态**必需且紧致**（u32 在 n·m ≥ 2^32 的测试点必溢出）。
//   · **(2) 号候选（收窄 `CAPP`）价值恒为 0**：`static constexpr CAPP5on = 1` ⇒ `else CAPP[...]`
//     全是死支 ⇒ 未引用的 static 被 GCC 丢弃。判题机 gcc 9.3 `-O2 -std=c++17` 汇编里
//     `CAPP` 引用 **0** 条 / `CAPP5` 5 条；本地 `nm` 符号表也只有 `CAPP5` ⇒ **它不在二进制里**，
//     工作集 0 字节、流量 0（旧账里那 2.40 MB 是重复计数）。
//   · **(3) 号候选（删冗余表示）没有对象**：写点唯一（同一 `val` 按 `CAPP5on` 二选一写），
//     三个读点读进同一变量 ⇒ `CAPP5 ≡ CAPP & 0xFFFFFFFFFF`，同一信息的两形态，且 `CAPP` 已被
//     constexpr 整条消掉。
//   · **[SENTINEL]（惰性建）实测否决**（`f17y_naive_gen.py`）：满规模 rand/chain 上
//     "值 == (x-1)*m+y 的纯函数" 占 **79.6% / 63.2%** ⇒ 可跳过 79.6%/63.2% 的**写**；
//     但 §2.19.867/§2.19.916「数行不数 uop」：每条 64 B 行装 12.8 条记录，跳过的写是**散布**的
//     ⇒ **100% 的行仍被弄脏**（1.50 MB 一行不省）⇒ 只省 store uop，不省足迹 ⇒ 不值一发。
//   · 于是改打**真正会减少行数**的一刀：查询表 2.40 MB → 1.50 MB（**37500 行 → 23438 行**），
//     且每查询的**载入数 2→1、存数 2→1**（一次 8 字节 memcpy 取回 (x,y) 两个字段：
//     `x = v & 0xFFFFF`、`y = (v>>20) & 0xFFFFF`；写侧一次 8 字节 memcpy 覆盖 5 字节 + 3 字节溢出，
//     溢出落在下一条的低位、随后被下一条自己的写覆盖，数组另留 8 字节余量 ⇒ 不越界）。
//
// 【合法性】本题 n,m ≤ 3×10^5 < 2^20 = 1048576（**3.5× 余量**）⇒ 20+20=40 位打包永不溢出 ✓
//   前瞻预取 `RINF[qxy_x(i+NF_PFD)]` 用的仍是同一条 8 字节取数（下标 i+6 ≤ q+5 ≤ 300005 ✓ 在界内）。
//
// 【§2.19.880 布局不变】新数组声明在 `QX`/`QY` 的原位置、占**相同的总字节数**（PN*8）
//   ⇒ 其后所有符号地址不变。**nm 实测**（base vs 本发，两二进制）：
//   `ARENA 0xc0050a0 / CAPP5 0x150050a0 / SMALLD 0x15173440 / RAPP 0x152983e0 /
//    BIGD 0x153bd380 / RINF 0x153fd380 / T4 0x15892200` —— **地址与尺寸全部逐位相同** ✓
//   ⇒ 本发的唯一变量就是查询表的表示 ✓
//
// 【闸门】**18/18 与基座逐字节相同**（`gen.py` 五模式 × 大小规模；覆盖 rand/chain/lastcol/
//   randx1/fewrows 五条路径 + n=3e5,m=1（全 y≥m 支）+ n=1,m=1,q=1 退化形状 + m=5 + 1000³）。
//   两种配置都编（本地 g++ 15.2 与 `tools/gcc93check.py` 的判题机 gcc 9.3，均 0 error）✓
//
// 【预期】省 0.90 MB 顺序流（QX/QY 2.40→1.50 MB、37500→23438 行）并每查询少一次载入/存数；
//   本题本机量具地板 ≈1.7~2.7% ⇒ 本地定时不可判读，**定价完全依赖判题机** ✓
// ★ 状态位：宽支红（B = 26.535983 > 1.005·T = 26.669074，T = 26.571198 ⇒ 严支线 26.306486）。
// ================

// ===== 基座件（[1] #108028 = `work/f17y_pfd6.cpp`）原头注，逐字保留其引用与取证 =====
// ===== REFERENCES =====
// [1] 本账号（saffah_cc_v41_agg1）在本工作区的提交：#102821
//     <https://duck.ac/submission/102821>（26.864711 ms，文件 `problems/noip17f/work/nf2_hoist2.cpp`）
//     = 本发的**引擎基座**（它的 [HOIST]/[HOIST2] 两把纯重排刀见该件头注与 notes 第十九轮）。
// [2] ★ duck.ac 用户 **saffah_codex_6s_agg2**，提交 **#107209**
//     <https://duck.ac/submission/107209>（noip17f 实时榜首 26.571198 ms = 本题 T）。
//     用途：本发**直接采用**该提交相对 [1] 的**唯一一处实质改动**（逐行核对见"思路"）——
//     **`CAPP5on` 做成 `static constexpr int = 1`（编译期常量 ⇒ 每次 CAPP 访问不再有那个运行期分支）
//     + 新增 `load_capp5()`：用一次 8 字节 `__builtin_memcpy` 取回 40 位压缩值（`& 0xFFFFFFFFFF`），
//     写侧同样一次 8 字节 `memcpy`**。该提交为公开源码，页面未附任何许可证声明；按本工作区惯例
//     在此注明账号、原始提交地址与所采用的内容。除这一处外，本发与该提交**逐字节相同**。
// [3] 本账号在本工作区的其它提交（本题的定价链）：#102808（[HOIST] −0.654%）、#102821（[HOIST2]
//     −2.65%）、#107229（[HOIST3] 判负 +3.43%）。
// ======================
// ===== 思路 =====
// ★ 本发是**单变量**：把 `CAPP5on` 从"运行期判定 + 手写 4+1 字节取数/存数"改成
//   **编译期常量 `static constexpr int CAPP5on = 1` + `load_capp5()` 的 8 字节 memcpy 取数**
//   （写侧同样一次 8 字节 `__builtin_memcpy`）。除此之外与 [1] 一字未动。
//
// 【取证（非注释行 diff，§2.19.719）】`[1]` 与 `[2]` 剥离注释后**只差这一处**（外加 6 处空行）：
//     `- static constexpr int CAPP5on = 1;  static inline u64 load_capp5(u32 jj){ memcpy 8B; & 0xFFFFFFFFFF }`
//     `+ static int CAPP5on;`（运行期 `CAPP5on = ((u64)n*(u64)m < (1ULL<<40))`）
//     `+ if (CAPP5on) { u32 lo_; memcpy(&lo_, CAPP5+5*jj, 4); return (u64)lo_ | ((u64)CAPP5[5*jj+4]<<32); }`
//   三个取数站点 + 一个写入站点都如此 ⇒ 每查询的 CAPP 访问少一次"载入常量+测试+分支"，
//   且取数从"两次小 memcpy + 移位 + 或"变成"一次 8 字节载入 + 一次掩码"。
//   ⇒ [2] 相对 [1] 的 1.09%（−0.2935 ms）应当全部来自这一处。
//   ★ 合法性：本题 n,m ≤ 3×10^5 ⇒ n·m ≤ 9×10^10 < 2^40 ⇒ 40 位压缩**永不溢出** ⇒
//     编译期 `= 1` 与运行期判定在本題数据上等价（CAPP5 数组另留 8 字节余量，故 8 字节读写不越界）。
//
// 【闸门】生产规模 5 组（`np17_rand.txt` n=m=q=3e5、`inst_rand_1000`、`inst_fewrows_300000`、
//   `inst_randx1_300000`、`inst_lastcol_300000`）+ `work/gen.py` 五模式×2 seed 共 10 组
//   ⇒ **15/15 与 [1] 输出逐字节相同** ✓（本题 n,m ≤ 3e5 下两者语义等价，见上）
// ⚠ 本题**本机量具地板 ≈1.7~2.7%**（同源码两二进制 min-of-13 交错：+1.69% / −0.85%）
//   ⇒ 本地定时不可判读；本发的定价完全依赖判题机。
// ★ 状态位：本题现在是"宽支红"（B = 26.864711 > 1.005·T = 26.705054）。按 §2.19.793，
//   **红题上提交更快的件没有额外惩罚**（严支缺口恰好减掉这把刀的价值），而且会把
//   `[X/1.005, T)` 这扇被动绿窗口**开出来**（不提交时它是空的）⇒ 本发即按此执行。
// ================
// ===== 参数扫描件（f17y_ 第 2 席，2026-09-28）=====
// 【这是什么】`NF_PFD = 4 → 6`（行描述符软件预取前瞻）。**只改这一个常量**，其余一字不动
//   （正文 = 我方当前最好件 #107523 = 对手 #107209 非注释逐字节复刻）。
// 【扫什么 / 未定价档】已定价档 {4,8,16,24,5}；本席上一发已给 `3`（读数 26.588482 = +0.015 ms ≈ 平偏负 ✗）。
//   本发给 **6**：对手 #107204→#107209 唯一动作是 NF_PFD 2→4 ⇒ 4 邻域曲线不平 ⇒ 6 未定价 ✓。
// 【预期方向】若 6 比 4 好 ⇒ 最优前瞻更长（链短但 MSL 压力大 ⇒ 偏发射/端口）；若更差 ⇒ 4 是拐点，{3,4,5,6} 四点可判型。
// 【目的】按目标原文"允许大量提交（含搜参数）"，用判题机正式提交给该邻域补未定价档（本机地板 2.74% ⇒ 本机不可判）。
#include <emmintrin.h>
#pragma GCC optimize("O3","no-tree-slp-vectorize")
#pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt,sse4.1,ssse3")
typedef unsigned char u8;
typedef unsigned short u16;
typedef unsigned u32;
typedef unsigned long long u64;
typedef long long i64;
#define NF_LAZY 1
// ===== nf3_engine.h  (engine template; wrapped into a namespace by nf3_gen.py) =====
// Base: problems/noip17f/work/hn_r20.cpp  (= current best #99566, 32.018 ms; its references:
// rival saffah_cc_v41_260924 #98371 / #99470 / #99533, and our own #99474).
// Variant knobs (set by the generator as -D macros around this text):
//   NF_LAZY      0/1 : do not compute the column value eagerly; store the column POSITION
//                      (a 20-bit reference) in the row's append slot and resolve the value
//                      only where it is actually needed (lazy construction / on-demand).
//   NF_SIMPLECLS 0/1 : drop the SIMPLE1 bitmap; every row class comes from the RINF tag
//                      (single 8-byte load, already software-prefetched) instead of a
//                      second random bitmap load.
//   NF_PFD          : software prefetch distance for RINF[QX[i+D]]  (0 = off)
//   NF_CAPP5       1 : enable the 40-bit compact column-append store (r20 declared CAPP5on
//                      but never assigned it, so it always used the 2.4 MB u64 array).
#ifndef NF_LAZY
#define NF_LAZY 0
#endif
#ifndef NF_SIMPLECLS
#define NF_SIMPLECLS 1
#endif
#ifndef NF_PFD
#define NF_PFD 6
#endif
#ifndef NF_CAPP5
#define NF_CAPP5 1
#endif
#ifndef NF_ARENA
#define NF_ARENA (144u << 20)
#endif

static const u8 *gip;
static u8 *gob;
static u32 g_n, g_m;              // for resolve()
#ifdef PROF
static unsigned long PT[16]; static int PTC;
static inline unsigned long rdt(){ unsigned a,d; __asm__ volatile("rdtsc":"=a"(a),"=d"(d)); return ((unsigned long)d<<32)|a; }
#define PTICK() PT[PTC++]=rdt()
#else
#define PTICK() ((void)0)
#endif

// ------------------------- fast input -------------------------
static const u64 MASKV[9] = {0ULL, 0xFFULL, 0xFFFFULL, 0xFFFFFFULL, 0xFFFFFFFFULL,
                             0xFFFFFFFFFFULL, 0xFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFULL,
                             0xFFFFFFFFFFFFFFFFULL};
static const u32 INV5[9] = {1u,        0xCCCCCCCDu, 0xC28F5C29u, 0x26E978D5u, 0x3AFB7E91u,
                            0x0BCBE61Du, 0x68C26139u, 0xAE8D46A5u, 0x22E90E21u};

static inline u32 rd() {
  for (;;) {
    u64 x;
    __builtin_memcpy(&x, gip, 8);
    u64 t = x ^ 0x3030303030303030ULL;
    u64 mm = ((t + 0x7676767676767676ULL) | t) & 0x8080808080808080ULL;
    u32 k = mm ? (u32)(__builtin_ctzll(mm) >> 3) : 8u;
    if (k == 0) { gip++; continue; }
    u64 d = t << ((8u - k) << 3);
    u64 c1 = (d * 10 + (d >> 8)) & 0x00FF00FF00FF00FFULL;
    u64 c2 = (c1 * 100 + (c1 >> 16)) & 0x0000FFFF0000FFFFULL;
    u64 c3 = (c2 * 10000 + (c2 >> 32));
    gip += k + 1;
    return (u32)c3;
  }
}

// ------------------------- fast output -------------------------
static const char D2[201] =
    "00010203040506070809101112131415161718192021222324252627282930313233343536373839"
    "40414243444546474849505152535455565758596061626364656667686970717273747576777879"
    "8081828384858687888990919293949596979899";

static u32 T4[10000];
static u64 POW10[20];
static u8  LB[65];
static u16 WI[2048];                  // [WLEN] WI[hi] = shift | (len << 8),  hi = v/1e8
static inline void writer_init() {
  for (u32 i = 0; i < 10000; i++) {
    u32 h = i / 100, l = i - h * 100;
    u8 *p = (u8 *)&T4[i];
    p[0] = (u8)D2[2*h]; p[1] = (u8)D2[2*h+1]; p[2] = (u8)D2[2*l]; p[3] = (u8)D2[2*l+1];
  }
  u64 p = 1; for (int i = 0; i < 20; i++) { POW10[i] = p; p *= 10; }
  for (u32 h = 1; h < 2048; h++) {                    // [WLEN]
    u32 d = 1; u64 t = 10; while (t <= h) { t *= 10; d++; }
    WI[h] = (u16)(((4u - d) << 3) | ((8u + d) << 8));
  }
  WI[0] = 0;
  for (int bl = 1; bl <= 64; bl++) {
    u64 lo = (bl == 1) ? 1ULL : (1ULL << (bl - 1));
    u32 d = 1; u64 t = 1; while (t * 10 <= lo) { t *= 10; d++; }
    LB[bl] = (u8)d;
  }
}
static inline u8 *wr_safe(u8 *o, u64 v) {
  u8 tmp[24];
  u32 i = 24;
  if (v < 10) { o[0] = (u8)('0' + v); o[1] = '\n'; return o + 2; }
  while (v >= 100) {
    u32 r = (u32)(v % 100);
    v /= 100;
    i -= 2;
    tmp[i] = D2[2 * r];
    tmp[i + 1] = D2[2 * r + 1];
  }
  if (v < 10) {
    tmp[--i] = (u8)('0' + v);
  } else {
    i -= 2;
    tmp[i] = D2[2 * v];
    tmp[i + 1] = D2[2 * v + 1];
  }
  u32 len = 24 - i;
  for (u32 w = 0; w < len; w++) o[w] = tmp[i + w];
  o[len] = '\n';
  return o + len + 1;
}
static inline u8 *wr(u8 *o, u64 v) {
  if (v < 10) { o[0] = (u8)('0' + v); o[1] = '\n'; return o + 2; }
  // ---- cut [W] (earlier round): no stack round-trip, leading 4-digit group is constant.
  // ---- cut [WLEN] (this round): ONE L1-resident table load replaces the serial
  //      lzcnt -> LB[bl] -> POW10[d0] -> cmp chain, and moves the leading-group lookup
  //      out of the 40 KB table (which does not fit L1D) into this 4 KiB one.
  u64 hv = v / 100000000ULL;
  if (hv - 1ULL >= 2047ULL) return wr_safe(o, v);     // v < 1e8 or v >= 2.048e11: rare
  u32 t = WI[(u32)hv];
  u32 len = t >> 8, lg = len - 8u;                    // lg = digits(hv) in [1,4]
  u32 lo8 = (u32)(v - hv * 100000000ULL);
  u32 a = lo8 / 10000, b = lo8 - a * 10000;
  u64 pa = ((u64)T4[a] << 32) | (u64)T4[(u32)hv];
  pa >>= ((u32)(t & 0xFFu));
  __builtin_memcpy(o, &pa, 8);
  __builtin_memcpy(o + len - 4, &T4[b], 4);
  o[len] = '\n';
  return o + len + 1;
}

// ------------------------- k-th alive -------------------------
static inline __m128i pf16(__m128i v) {
  v = _mm_add_epi16(v, _mm_slli_si128(v, 2));
  v = _mm_add_epi16(v, _mm_slli_si128(v, 4));
  v = _mm_add_epi16(v, _mm_slli_si128(v, 8));
  return v;
}
static inline __m128i gt16u(__m128i a, __m128i b) {
  const __m128i sg_ = _mm_set1_epi16((short)0x8000);
  return _mm_cmpgt_epi16(_mm_xor_si128(a, sg_), _mm_xor_si128(b, sg_));
}
static inline u32 sel8(const u16 *p, u32 rem, u32 *sub) {
  __m128i inc = pf16(_mm_loadu_si128((const __m128i *)p));
  u32 msk = (u32)_mm_movemask_epi8(gt16u(inc, _mm_set1_epi16((short)(rem - 1))));
  u32 j = (u32)__builtin_ctz(msk) >> 1;
  u16 buf[8];
  _mm_storeu_si128((__m128i *)buf, _mm_slli_si128(inc, 2));
  *sub = (u32)buf[j];
  return j;
}
static inline u32 sel8w(const u8 *pw, u32 rem, u32 *sub) {
  __m128i b8 = _mm_loadl_epi64((const __m128i *)pw);
  __m128i a = _mm_sub_epi16(_mm_set1_epi16(64), _mm_unpacklo_epi8(b8, _mm_setzero_si128()));
  __m128i inc = pf16(a);
  u32 msk = (u32)_mm_movemask_epi8(gt16u(inc, _mm_set1_epi16((short)(rem - 1))));
  u32 j = (u32)__builtin_ctz(msk) >> 1;
  u16 buf[8];
  _mm_storeu_si128((__m128i *)buf, _mm_slli_si128(inc, 2));
  *sub = (u32)buf[j];
  return j;
}
static inline u32 kth_alive(const u64 *del, const u8 *wc, const u16 *bc, const u16 *gs, const u16 *sg, u32 k) {
  u32 rem = k, s = 0;
  while (rem > (u32)sg[s]) { rem -= sg[s]; s++; }
  u32 sub;
  u32 jg = sel8(gs + (s << 3), rem, &sub); rem -= sub;
  u32 g = (s << 3) + jg;
  u32 jb = sel8(bc + (g << 3), rem, &sub); rem -= sub;
  u32 b = (g << 3) + jb;
  u32 sub2;
  u32 wi = sel8w(wc + (b << 3), rem, &sub2); rem -= sub2;
  u32 base = (b << 9) + (wi << 6);
  u64 m = ~del[(b << 3) + wi];
  u64 r; __asm__("pdep %2, %1, %0" : "=r"(r) : "r"(1ULL << (rem - 1)), "r"(m));
  return base + (u32)__builtin_ctzll(r) + 1;
}
static inline void big_del(u64 *del, u8 *wc, u16 *bc, u16 *gs, u16 *sg, u32 p) {
  u32 w = p >> 6;
  u32 b = w >> 3, g = b >> 3, s = g >> 3;
  del[w] |= 1ULL << (p & 63);
  wc[w]++; bc[b]--; gs[g]--; sg[s]--;
}
// ---- [RIVAL-FUSED] kth_alive + big_del in ONE function -------------------------------
// Copied from duck.ac user saffah_cc_v41_260924, submission #100076 (their current rank-1,
// 30.191 ms), which gained -5.7% over their previous generation (#99562 -> #100076) with
// this single change.  Rationale (their comment, condensed): the deletion's (word, block,
// group, super) indices are EXACTLY the ones the select already produced, so big_del's four
// SERIAL shifts (w=p>>6, b=w>>3, g=b>>3, s=g>>3) are re-derivations of values already in
// registers -- and they sat on the critical path of a chain that runs once per query.
static inline u32 kth_alive_del(u64 *del, u8 *wc, u16 *bc, u16 *gs, u16 *sg, u32 k) {
  u32 rem = k, s = 0;
  while (rem > (u32)sg[s]) { rem -= sg[s]; s++; }
  u32 sub;
  u32 jg = sel8(gs + (s << 3), rem, &sub); rem -= sub;
  u32 g = (s << 3) + jg;
  u32 jb = sel8(bc + (g << 3), rem, &sub); rem -= sub;
  u32 b = (g << 3) + jb;
  u32 sub2;
  u32 wi = sel8w(wc + (b << 3), rem, &sub2); rem -= sub2;
  u32 w = (b << 3) + wi;
  u64 m = ~del[w];
  u64 r; __asm__("pdep %2, %1, %0" : "=r"(r) : "r"(1ULL << (rem - 1)), "r"(m));
  u32 bit = (u32)__builtin_ctzll(r);
  del[w] |= r;
  wc[w]++; bc[b]--; gs[g]--; sg[s]--;
  return ((b << 9) + (wi << 6)) + bit + 1;
}
static inline unsigned long ka_need(u32 V) {
  u32 nwords = (V + 63) >> 6;
  u32 nblk = (nwords + 7) >> 3;
  u32 ngrp = (nblk + 7) >> 3;
  u32 nsup = (ngrp + 7) >> 3;
  u32 nbp = ngrp << 3, ngp = nsup << 3;
  unsigned long need = ((unsigned long)nwords << 3) + nwords + 1;
  need = (need + 1) & ~1UL; need += (((unsigned long)nbp) << 1) + 2;
  need = (need + 1) & ~1UL; need += (((unsigned long)ngp) << 1) + 2;
  need = (need + 1) & ~1UL; need += (((unsigned long)nsup) << 1) + 2;
  return (need + 63) & ~(unsigned long)63;
}
static inline unsigned long big_init(u8 *mem, u32 V, u64 **pdel, u8 **pwc,
                                     u16 **pbc, u16 **pgs, u16 **psg) {
  u32 nwords = (V + 63) >> 6;
  u32 nblk = (nwords + 7) >> 3;
  u32 ngrp = (nblk + 7) >> 3;
  u32 nsup = (ngrp + 7) >> 3;
  u32 nbp = ngrp << 3, ngp = nsup << 3;
  unsigned long o1 = (((unsigned long)nwords << 3) + 1) & ~1UL;
  unsigned long o2 = (o1 + nwords + 1) & ~1UL;
  unsigned long o3 = (o2 + (((unsigned long)nbp) << 1) + 1) & ~1UL;
  unsigned long o4 = (o3 + (((unsigned long)ngp) << 1) + 1) & ~1UL;
  u64 *del = (u64 *)mem;
  u8  *wc  = (u8 *)(mem + o1);
  u16 *bc  = (u16 *)(mem + o2);
  u16 *gs  = (u16 *)(mem + o3);
  u16 *sg  = (u16 *)(mem + o4);
  for (u32 i = 0; i < nwords; i++) { del[i] = 0; wc[i] = 0; }
  u32 hi = V & 63;
  if (hi) { del[nwords - 1] = ~0ULL << hi; wc[nwords - 1] = (u8)(64 - hi); }
  for (u32 i = 0; i < nbp; i++) bc[i] = 0;
  for (u32 i = 0; i < ngp; i++) gs[i] = 0;
  for (u32 i = 0; i < nsup; i++) sg[i] = 0;
  for (u32 i = 0; i < nwords; i++) bc[i >> 3] += (u16)(64u - (u32)wc[i]);
  for (u32 i = 0; i < nblk; i++)  gs[i >> 3] += bc[i];
  for (u32 i = 0; i < ngrp; i++)  sg[i >> 3] += gs[i];
  *pdel = del; *pwc = wc; *pbc = bc; *pgs = gs; *psg = sg;
  return ka_need(V);
}

static inline u32 small_remove(u32 *R, u32 d, u32 k) {
  u32 lo = 0, hi = d;
  while (lo < hi) {
    u32 mid = (lo + hi + 1) >> 1;
    if (R[mid - 1] - mid < k) lo = mid; else hi = mid - 1;
  }
  u32 p = k + lo;
  if (lo < d) {
    u32 *s = R + d, *e = R + lo;
    while (s > e) { *s = s[-1]; s--; }
  }
  R[lo] = p;
  return p;
}

// ------------------------- globals -------------------------
#define PN 300005
/* [QXY5] one packed query list: record k lives at byte 5*k, v = x | (y<<20).
   Same total bytes as the old QX+QY pair (PN*8) so that every later BSS symbol keeps its
   address (verified with nm: RINF/CAPP5/RAPP/SMALLD/ARENA/T4/BIGD all unchanged); only the
   first PN*5+8 bytes are ever touched.  x,y <= 3e5 < 2^20 (3.5x margin). */
static u8 QXY[PN * 8];
static inline void qxy_load(u32 k, u32 &x, u32 &y) {
  u64 v; __builtin_memcpy(&v, QXY + (size_t)k * 5, 8);
  x = (u32)(v & 0xFFFFFu); y = (u32)((v >> 20) & 0xFFFFFu);
}
static inline void qxy_store(u32 k, u32 x, u32 y) {
  u64 v = (u64)x | ((u64)y << 20);
  __builtin_memcpy(QXY + (size_t)k * 5, &v, 8);
}
static inline u32 qxy_x(u32 k) { u64 v; __builtin_memcpy(&v, QXY + (size_t)k * 5, 8); return (u32)(v & 0xFFFFFu); }
struct RINF_T { u32 offb; u32 appn; };
static RINF_T RINF[PN];
static u64 SIMPLE1[(PN + 63) / 64];
static u32 BIGD[8192][8];
#if NF_LAZY
static u32 RAPP[PN];                  // NF_LAZY: stores a column POSITION reference (<= n+q)
#else
static u64 RAPP[PN];                  // stores the column value
#endif
static u32 SMALLD[PN];
static u64 CAPP[PN];
static u8  CAPP5[PN * 5 + 8];
static constexpr int CAPP5on = 1;
static inline u64 load_capp5(u32 jj) { u64 v; __builtin_memcpy(&v, CAPP5 + (size_t)jj * 5, 8); return v & 0xFFFFFFFFFFULL; }

#ifndef NF_ARENA
#define NF_ARENA (144u << 20)
#endif
#define ARENASZ ((unsigned long)NF_ARENA)
static u8 ARENA[NF_ARENA];

static u64 *CDEL; static u8 *CWC; static u16 *CBC; static u16 *CGS; static u16 *CSG;

#if NF_LAZY
// Resolve a column POSITION p to the value living there.  Called only on the rare paths
// where the answer really is a column-appended value (p > n): deferred construction.
static inline u64 resolve(u32 p) {
  if (p <= g_n) return (u64)p * g_m;
  u32 jj = p - g_n - 1;
  if (CAPP5on) return load_capp5(jj);
  return CAPP[jj];
}
#endif

// returns output length; PT[0..3] = phase ticks when PROF
static unsigned long nf_solve(u8 *out) {
#ifdef PROF
  PTC = 0;
#endif
  writer_init();
  PTICK();
  u32 n = rd(), m = rd(), q = rd();
  g_n = n; g_m = m;

  u32 mm1 = m - 1;
  // ---- phase 1 ----
  for (u32 i = 0; i < q; i++) {
    u32 x = rd(), y = rd();
    qxy_store(i, x, y);
    if (y < m) SMALLD[x]++;
  }
  PTICK();
  // ---- phase 2 ----
  u32 off = 0;
  u32 nbig = 0;
  unsigned long asz = 0;
  for (u32 r = 1; r <= n; r++) {
    u32 c = SMALLD[r];
    if (!c) continue;
#if NF_SIMPLECLS
    if (c == 1) { RINF[r].offb = (0x1FFEu << 19); RINF[r].appn = 0; continue; }
#else
    if (c == 1) { SIMPLE1[r >> 6] |= 1ULL << (r & 63); continue; }
#endif
    if (c == 2) { RINF[r].offb = (0x1FFFu << 19); RINF[r].appn = 0; continue; }
    u32 tag = 0;
    u64 V = (u64)mm1 + c;
    i64 cs = (i64)c * ((i64)(c >> 3) + 30);
    i64 cb = (i64)((V >> 6) + 1) * 2 + (i64)c * 55;
    if (cb < cs && nbig < 8190) {
      unsigned long need = ka_need((u32)V);
      if (asz + need <= ARENASZ - (1u << 20)) {
        u64 *pdel; u8 *pwc; u16 *pbc; u16 *pgs; u16 *psg;
        big_init(ARENA + asz, (u32)V, &pdel, &pwc, &pbc, &pgs, &psg);
        u32 *D = BIGD[nbig];
        D[0] = (u32)((u8 *)pdel - ARENA); D[1] = (u32)((u8 *)pwc - ARENA);
        D[2] = (u32)((u8 *)pbc - ARENA);  D[3] = (u32)((u8 *)pgs - ARENA);
        D[4] = (u32)((u8 *)psg - ARENA);
        asz += need;
        tag = ++nbig;
      }
    }
    RINF[r].offb = (off & 0x7FFFFu) | (tag << 19);
    RINF[r].appn = 0;
    off += c;
  }
  PTICK();
  // ---- column ----
  {
    u64 *pdel; u8 *pwc; u16 *pbc; u16 *pgs; u16 *psg;
    unsigned long need = big_init(ARENA + asz, n + q, &pdel, &pwc, &pbc, &pgs, &psg);
    asz += need;
    CDEL = pdel; CWC = pwc; CBC = pbc; CGS = pgs; CSG = psg;
  }
  PTICK();
  // ---- phase 3 ----
  u32 cappn = 0;
  u8 *o = out;
  for (u32 i = 0; i < q; i++) {
    u32 x, y; qxy_load(i, x, y);
#if NF_PFD > 0
    if (i + NF_PFD < q) __builtin_prefetch(&RINF[qxy_x(i + NF_PFD)], 0, 3);
#endif
    // [HOIST] row-descriptor load, issued before the column select (see header)
    u32 hoffb = 0, happn = 0;
    if (y < m) { hoffb = RINF[x].offb; happn = RINF[x].appn; }
    // [HOIST2] the c>=3 row path's position computation is also pc-independent: start it now so
    // its SMALLD/arena latency overlaps the select chain instead of following it.
    u32 ho3 = 0, hopp = 0;
    if (y < m) {
      u32 t2 = hoffb >> 19;
      if (t2 != 0x1FFEu && t2 != 0x1FFFu) {   // t2 == 0 is the c>=3 SMALL row
        u32 ro2 = hoffb & 0x7FFFFu, ap2 = happn;
        if (t2) {
          const u32 *D = BIGD[t2 - 1];
          u64 *pdel = (u64 *)(ARENA + D[0]); u8 *pwc = (u8 *)(ARENA + D[1]);
          u16 *pbc = (u16 *)(ARENA + D[2]); u16 *pgs = (u16 *)(ARENA + D[3]);
          u16 *psg = (u16 *)(ARENA + D[4]);
          hopp = kth_alive_del(pdel, pwc, pbc, pgs, psg, y);
        } else {
          hopp = small_remove(SMALLD + ro2, ap2, y);
        }
        ho3 = 1;
      }
    }
    u32 pc = kth_alive_del(CDEL, CWC, CBC, CGS, CSG, x);
#if !NF_LAZY
    u64 cval;
    if (pc <= n) cval = (u64)pc * m;
    else {
      u32 jj = pc - n - 1;
      if (CAPP5on) cval = load_capp5(jj);
      else cval = CAPP[jj];
    }
#endif
    u64 val;
    if (y < m) {
      u32 r = x;
#if !NF_SIMPLECLS
      if ((SIMPLE1[r >> 6] >> (r & 63)) & 1ULL) {
        val = (u64)(r - 1) * m + y;
      } else {
#endif
      u32 offb = hoffb;                 // [HOIST] loaded above, in parallel with the select
      u32 t = offb >> 19;
      u32 ro = offb & 0x7FFFFu;
      u32 ap = happn;
      u32 pp;
#if NF_SIMPLECLS
      if (t == 0x1FFEu) {
        val = (u64)(r - 1) * m + y;
      } else
#endif
      if (t == 0x1FFFu) {
        u32 p0 = offb & 0x7FFFFu;
        if (!p0) {
          pp = y;
          RINF[r].offb = (0x1FFFu << 19) | y;
          RINF[r].appn = pc + 1;
          val = (u64)(r - 1) * m + pp;
        } else {
          pp = y + (y >= p0 ? 1u : 0u);
          if (pp <= mm1) val = (u64)(r - 1) * m + pp;
          else {
            u32 pcc = RINF[r].appn - 1;
#if NF_LAZY
            val = resolve(pcc);
#else
            if (pcc <= n) val = (u64)pcc * m;
            else { u32 jj = pcc - n - 1;
              if (CAPP5on) val = load_capp5(jj);
              else val = CAPP[jj];
            }
#endif
          }
        }
      } else {
        (void)ro; (void)ap;
        pp = ho3 ? hopp : 0;              // [HOIST2] computed above; ho3==1 on every path here
#if NF_LAZY
        u64 rv = (pp <= mm1) ? ((u64)(r - 1) * m + pp) : resolve(RAPP[ro + (pp - m)]);
        RAPP[ro + ap] = pc;                    // store the POSITION reference, not the value
        val = rv;
#else
        val = (pp <= mm1) ? ((u64)(r - 1) * m + pp) : RAPP[ro + (pp - m)];
        RAPP[ro + ap] = cval;
#endif
        RINF[r].appn = ap + 1;
      }
#if !NF_SIMPLECLS
      }
#endif
    } else {
#if NF_LAZY
      val = resolve(pc);
#else
      val = cval;
#endif
    }
    { size_t o_ = (size_t)cappn * 5;
      if (CAPP5on) __builtin_memcpy(CAPP5 + o_, &val, 8);
      else CAPP[cappn] = val; }
    cappn++;
    o = (i + 1 == q) ? wr_safe(o, val) : wr(o, val);
  }
  PTICK();
  return (unsigned long)(o - out);
}

static unsigned long nf_run(const u8 *in, u8 *out) { gip = in; return nf_solve(out); }

struct DUCKDI{unsigned long abi;const char*sp;unsigned long sn;char*op;unsigned long ol,os;char*ep;unsigned long el,es;const char*IB;unsigned long IBl;char*OB;unsigned long OBl;unsigned long tsc;}__attribute__((packed));
extern "C" void __libc_start_main(void*m,int argc,char**argv){
 unsigned long*p=(unsigned long*)(argv+argc+1);while(*p)p++;p++;
 DUCKDI*d=0;for(;p[0];p+=2)if(p[0]==0x6b637564UL){d=(DUCKDI*)p[1];break;}
 gip=(const u8*)d->sp; gob=(u8*)d->op;
 unsigned long olen = nf_solve(gob);
 gob=(u8*)d->op+olen;
 d->os=olen;
 __asm__ volatile("syscall"::"a"(60),"D"(0):"rcx","r11","memory");
 for(;;);
}
int main(){return 0;}

评测结果