test/stirling_number_of_first_kind_small_p_large_n.test.cpp

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• Last update: 2025-02-27 21:36:01+08:00
• Problem: https://judge.yosupo.jp/problem/stirling_number_of_the_first_kind_small_p_large_n

Depends on

• combi/stirlingFirstModP.cpp
• default/t.cpp
• modint/dynamicSimpleMint.cpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/stirling_number_of_the_first_kind_small_p_large_n"

#include "../default/t.cpp"
#include "../modint/dynamicSimpleMint.cpp"
#include "../combi/stirlingFirstModP.cpp"

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int t, p; cin >> t >> p;
  mint::set_mod(p);
  stirlingFirstModP<mint> stir;
  while(t--) {
    ll n, k; cin >> n >> k;
    cout << stir.s(n, k) << '\n';
  }

  return 0;
}

#line 1 "test/stirling_number_of_first_kind_small_p_large_n.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/stirling_number_of_the_first_kind_small_p_large_n"

#line 1 "default/t.cpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>

#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)

#define clock chrono::steady_clock::now().time_since_epoch().count()

using namespace std;

template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2> pr) {
  return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
  for(size_t i = 0; T x : arr) {
    os << x;
    if (++i != N) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
  for(size_t i = 0; T x : vec) {
    os << x;
    if (++i != size(vec)) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
  for(size_t i = 0; T x : s) {
    os << x;
    if (++i != size(s)) os << ' ';
  }
  return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2> &m) {
  for(size_t i = 0; pair<T1, T2> x : m) {
    os << x;
    if (++i != size(m)) os << ' ';
  }
  return os;
}

#ifdef DEBUG
#define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__)
template<typename T> void _do(T &&x) { cerr << x; }
template<typename T, typename ...S> void _do(T &&x, S&&...y) { cerr << x << ", "; _do(y...); }
template<typename T> void _do2(T &&x) { cerr << x << endl; }
template<typename T, typename ...S> void _do2(T &&x, S&&...y) { cerr << x << ", "; _do2(y...); }
#else
#define dbg(...)
#endif

using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

template<typename T> using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T> using max_heap = priority_queue<T>;

template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP = plus<T>>
void pSum(rng &v) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = OP()(p, x);
}
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP>
void pSum(rng &v, OP op) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = op(p, x);
}

template<ranges::forward_range rng>
void Unique(rng &v) {
  ranges::sort(v);
  v.resize(unique(v.begin(), v.end()) - v.begin());
}

template<ranges::random_access_range rng>
rng invPerm(rng p) {
  rng ret = p;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = i;
  return ret;
}

template<ranges::random_access_range rng, ranges::random_access_range rng2>
rng Permute(rng v, rng2 p) {
  rng ret = v;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = v[i];
  return ret;
}

template<bool directed>
vector<vector<int>> readGraph(int n, int m, int base) {
  vector<vector<int>> g(n);
  for(int i = 0; i < m; i++) {
    int u, v; cin >> u >> v;
    u -= base, v -= base;
    g[u].emplace_back(v);
    if constexpr (!directed)
      g[v].emplace_back(u);
  }
  return g;
}

template<class T>
void setBit(T &msk, int bit, bool x) {
  msk = (msk & ~(T(1) << bit)) | (T(x) << bit);
}
template<class T> void flipBit(T &msk, int bit) { msk ^= T(1) << bit; }
template<class T> bool getBit(T msk, int bit) { return msk >> bit & T(1); }

template<class T>
T floorDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? a / b : (a - b + 1) / b;
}
template<class T>
T ceilDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? (a + b - 1) / b : a / b;
}

template<class T> bool chmin(T &a, T b) { return a > b ? a = b, 1 : 0; }
template<class T> bool chmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
#line 1 "modint/dynamicSimpleMint.cpp"
template<uint32_t ver>
struct simpleMint {
  using mint = simpleMint;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static u32 mod;

  static constexpr u32 get_mod() { return mod; }
  static void set_mod(u32 _mod) { mod = _mod; }

  simpleMint() : a(0) {}
  simpleMint(const int64_t &b) : a((b % mod + mod) % mod) {}

  u32 a;

  mint pow(u64 k) const {
    mint res(1), base(*this);
    while(k) {
      if (k & 1)
        res *= base;
      base *= base, k >>= 1;
    }
    return res;
  }

  mint inverse() const { return (*this).pow(mod - 2); }
  u32 get() const { return a; }

  mint& norm() {
    a = (a >= mod ? a - mod : a < 0 ? a + mod : a);
    return *this;
  }

  mint& operator+=(mint b) {
    a += b.a;
    return (*this).norm();
  }
  mint& operator-=(mint b) {
    if (b.a > a) a = a + mod - b.a;
    else a -= b.a;
    return (*this).norm();
  }
  mint& operator*=(mint b) {
    a = (u64(a) * b.a) % mod;
    return *this;
  }
  mint& operator/=(mint b) {
    a = (u64(a) * b.inverse().a) % mod;
    return *this;
  }

  mint operator-() { return mint() - mint(*this); }
  bool operator==(mint b) { return a == b.a; }
  bool operator!=(mint b) { return a != b.a; }
  
  friend mint operator+(mint c, mint d) { return c += d; }
  friend mint operator-(mint c, mint d) { return c -= d; }
  friend mint operator*(mint c, mint d) { return c *= d; }
  friend mint operator/(mint c, mint d) { return c /= d; }

  friend ostream& operator<<(ostream& os, const mint& b) {
    return os << b.a;
  }
  friend istream& operator>>(istream& is, mint& b) {
    int64_t val;
    is >> val;
    b = mint(val);
    return is;
  }
};

template<> uint32_t simpleMint<0>::mod = 2;
using mint = simpleMint<0>;
#line 1 "combi/stirlingFirstModP.cpp"
//#include<modint/MontgomeryModInt.cpp>

template<class Mint>
struct stirlingFirstModP {
  const int p;
  vector<vector<Mint>> _s, _c;
  stirlingFirstModP() : p(Mint::get_mod()),
    _s(p, vector<Mint>(p)), _c(p, vector<Mint>(p)) {
    for(int i = 0; i < p; i++) {
      for(int j = 1; j < i; j++)
        _s[i][j] = _s[i - 1][j - 1] + _s[i - 1][j] * -(i - 1);
      _s[i][i] = 1;
    }
    for(int i = 0; i < p; i++) {
      _c[i][0] = 1;
      for(int j = 1; j < i; j++)
        _c[i][j] = _c[i - 1][j - 1] + _c[i - 1][j];
      _c[i][i] = 1;
    }
  }

  Mint binom(int64_t n, int64_t k) {
    if (k < 0 or n < k) return Mint(0);
    Mint r = 1;
    while(n)
      r *= _c[n % p][k % p], n /= p, k /= p;
    return r;
  }

  Mint s(int64_t n, int64_t k) {
    int64_t i = n / p, j = n % p;
    int64_t b = ((k - i) % (p - 1) + (p - 1)) % (p - 1);
    int64_t a = (k - i - b) / (p - 1);
    mint r = binom(i, a) * ((i - a) % 2 == 1 ? -1 : 1) * _s[j][b];
    if (b == 0 and a > 0)
      r += binom(i, a - 1) * ((i - a + 1) % 2 == 1 ? -1 : 1) * _s[j][p - 1];
    return r;
  }
};
#line 6 "test/stirling_number_of_first_kind_small_p_large_n.test.cpp"

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int t, p; cin >> t >> p;
  mint::set_mod(p);
  stirlingFirstModP<mint> stir;
  while(t--) {
    ll n, k; cin >> n >> k;
    cout << stir.s(n, k) << '\n';
  }

  return 0;
}

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