結果

問題 No.1025 Modular Equation
ユーザー kyort0n
提出日時 2020-04-10 22:56:45
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 6,637 bytes
コンパイル時間 2,770 ms
コンパイル使用メモリ 201,500 KB
実行使用メモリ 19,564 KB
最終ジャッジ日時 2024-09-15 23:21:29
合計ジャッジ時間 9,525 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 6 TLE * 1 -- * 25
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> l_l;
typedef pair<int, int> i_i;
template<class T>
inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}

const long double EPS = 1e-10;
const long long INF = 1e18;
const long double PI = acos(-1.0L);
//const ll mod = 1000000007;

#include <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <cassert>
#include <fstream>
#include <utility>
#include <functional>
#include <time.h>
#include <stack>
#include <array>
#define popcount __builtin_popcount
using namespace std;
typedef long long int ll;
typedef pair<int, int> P;
ll powmod(ll a, ll k, ll mod){
    ll ap=a, ans=1;
    while(k){
        if(k&1){
            ans*=ap;
            ans%=mod;
        }
        ap=ap*ap;
        ap%=mod;
        k>>=1;
    }
    return ans;
}
ll inv(ll a, ll mod){
    return powmod(a, mod-2, mod);
}

template <class Z> Z getint() {
  char c = getchar();
  bool neg = c == '-';
  Z res = neg ? 0 : c - '0';
  while (isdigit(c = getchar())) res = res * 10 + (c - '0');
  return neg ? -res : res;
}
template <class Z> void putint(Z a, char c = '\n') {
  if (a < 0) putchar('-'), a = -a;
  int d[40], i = 0;
  do d[i++] = a % 10; while (a /= 10);
  while (i--) putchar('0' + d[i]);
  putchar(c);
}

template <class T, class F = multiplies<T>>
T power(T a, long long n, F op = multiplies<T>(), T e = {1}) {
  assert(n >= 0);
  T res = e;
  while (n) {
    if (n & 1) res = op(res, a);
    if (n >>= 1) a = op(a, a);
  }
  return res;
}

template <unsigned Mod> struct Modular {
  using M = Modular;
  unsigned v;
  Modular(long long a = 0) : v((a %= Mod) < 0 ? a + Mod : a) {}
  M operator-() const { return M() -= *this; }
  M& operator+=(M r) { if ((v += r.v) >= Mod) v -= Mod; return *this; }
  M& operator-=(M r) { if ((v += Mod - r.v) >= Mod) v -= Mod; return *this; }
  M& operator*=(M r) { v = (uint64_t)v * r.v % Mod; return *this; }
  M& operator/=(M r) { return *this *= power(r, Mod - 2); }
  friend M operator+(M l, M r) { return l += r; }
  friend M operator-(M l, M r) { return l -= r; }
  friend M operator*(M l, M r) { return l *= r; }
  friend M operator/(M l, M r) { return l /= r; }
  friend bool operator==(M l, M r) { return l.v == r.v; }
};

template <unsigned Mod> void ntt(vector<Modular<Mod>>& a, bool inverse) {
  static vector<Modular<Mod>> dw(30), idw(30);
  if (dw[0] == 0) {
    Modular<Mod> root = 2;
    while (power(root, (Mod - 1) / 2) == 1) root += 1;
    for (int i = 0; i < 30; ++i)
      dw[i] = -power(root, (Mod - 1) >> (i + 2)), idw[i] = 1 / dw[i];
  }
  int n = a.size();
  assert((n & (n - 1)) == 0);
  if (not inverse) {
    for (int m = n; m >>= 1; ) {
      Modular<Mod> w = 1;
      for (int s = 0, k = 0; s < n; s += 2 * m) {
        for (int i = s, j = s + m; i < s + m; ++i, ++j) {
          auto x = a[i], y = a[j] * w;
          if (x.v >= Mod) x.v -= Mod;
          a[i].v = x.v + y.v, a[j].v = x.v + (Mod - y.v);
        }
        w *= dw[__builtin_ctz(++k)];
      }
    }
  } else {
    for (int m = 1; m < n; m *= 2) {
      Modular<Mod> w = 1;
      for (int s = 0, k = 0; s < n; s += 2 * m) {
        for (int i = s, j = s + m; i < s + m; ++i, ++j) {
          auto x = a[i], y = a[j];
          a[i] = x + y, a[j].v = x.v + (Mod - y.v), a[j] *= w;
        }
        w *= idw[__builtin_ctz(++k)];
      }
    }
  }
  auto c = 1 / Modular<Mod>(inverse ? n : 1);
  for (auto&& e : a) e *= c;
}
template <unsigned Mod>
vector<Modular<Mod>> operator*(vector<Modular<Mod>> l, vector<Modular<Mod>> r) {
  if (l.empty() or r.empty()) return {};
  int n = l.size(), m = r.size(), sz = 1 << __lg(2 * (n + m - 1) - 1);
  if (min(n, m) < 30) {
    vector<long long> res(n + m - 1);
    for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j)
      res[i + j] += (l[i] * r[j]).v;
    return {begin(res), end(res)};
  }
  bool eq = l == r;
  l.resize(sz), ntt(l, false);
  if (eq) r = l;
  else r.resize(sz), ntt(r, false);
  for (int i = 0; i < sz; ++i) l[i] *= r[i];
  ntt(l, true), l.resize(n + m - 1);
  return l;
}

constexpr long long mod = 1e9 + 7;
using Mint = Modular<mod>;

vector<Mint> operator*(const vector<Mint>& l, const vector<Mint>& r) {
  if (l.empty() or r.empty()) return {};
  int n = l.size(), m = r.size();
  static constexpr int mod0 = 998244353, mod1 = 1300234241, mod2 = 1484783617;
  using Mint0 = Modular<mod0>;
  using Mint1 = Modular<mod1>;
  using Mint2 = Modular<mod2>;
  vector<Mint0> l0(n), r0(m);
  vector<Mint1> l1(n), r1(m);
  vector<Mint2> l2(n), r2(m);
  for (int i = 0; i < n; ++i) l0[i] = l[i].v, l1[i] = l[i].v, l2[i] = l[i].v;
  for (int j = 0; j < m; ++j) r0[j] = r[j].v, r1[j] = r[j].v, r2[j] = r[j].v;
  l0 = l0 * r0, l1 = l1 * r1, l2 = l2 * r2;
  vector<Mint> res(n + m - 1);
  static const Mint1 im0 = 1 / Mint1(mod0);
  static const Mint2 im1 = 1 / Mint2(mod1), im0m1 = im1 / mod0;
  static const Mint m0 = mod0, m0m1 = m0 * mod1;
  for (int i = 0; i < n + m - 1; ++i) {
    int y0 = l0[i].v;
    int y1 = (im0 * (l1[i] - y0)).v;
    int y2 = (im0m1 * (l2[i] - y0) - im1 * y1).v;
    res[i] = y0 + m0 * y1 + m0m1 * y2;
  }
  return res;
}
using Mint = Modular<mod>;

int main() {
    //cout.precision(10);
    cin.tie(0);
    ios::sync_with_stdio(false);
    ll p, n, k, b;
    cin >> p >> n >> k >> b;
    vector<ll> x(p);
    for(int i = 0; i < p; i++) {
        x[i] = powmod(i, k, p);
    }
    vector<Mint> v(p);
    v[0] = 1;
    for(int i = 0; i < n; i++) {
        ll a;
        cin >> a;
        //cerr << i << " " << a << endl;
        vector<Mint> w(p);
        for(ll i = 0; i < p; i++) {
            w[x[i] * a % p] += 1;
        }
        /*
        cerr << "w: ";
        for(int i = 0; i < p; i++) {
          cerr << w[i] << " ";
        }
        cerr << endl;
        */
        v = v * w;
        /*
        for(auto val : v) {
            cerr << val << " ";
        }
        cerr << endl;
        */
        for(int i = p; i < v.size(); i++) {
            v[i-p] += v[i];
        }
        v.resize(p);
        /*
        for(auto val : v) {
            cerr << val << " ";
        }
        cerr << endl;
        */
    }
    ll ans = v[b].v;
    cout << ans << endl;
    //cout << v[b] << endl;
    return 0;
}
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