#358740 (C++14) No.8046 yukicoderの過去問

• 問題: No.8046 yukicoderの過去問
• ユーザー: hashiryo
• 提出日時: 2019-07-10 21:59:38
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 125 ms / 2,000 ms
• コード長: 11,116 bytes
• コンパイル時間: 1,997 ms
• コンパイル使用メモリ: 181,548 KB
• 実行使用メモリ: 10,224 KB
• 最終ジャッジ日時: 2024-11-06 08:55:48
• 合計ジャッジ時間: 3,721 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	114 ms; 10,208 KB
testcase_01	AC	114 ms; 10,092 KB
testcase_02	AC	114 ms; 10,092 KB
testcase_03	AC	115 ms; 10,220 KB
testcase_04	AC	116 ms; 10,220 KB
testcase_05	AC	116 ms; 10,220 KB
testcase_06	AC	125 ms; 10,184 KB
testcase_07	AC	118 ms; 10,224 KB
testcase_08	AC	122 ms; 10,096 KB

ソースコード

#include<bits/stdc++.h>

#define debug(x) cerr << #x << ": " << x << endl
#define debugArray(x,n) for(long long hoge = 0; (hoge) < (n); ++ (hoge)) cerr << #x << "[" << hoge << "]: " << x[hoge] << endl
using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef vector<ll> vll;
const ll INF = LLONG_MAX/2;
const ll MOD = 1e9+7;

using u32 = unsigned;
using u64 = unsigned long long;

namespace ntt {

template <u64 mod, u64 prim_root>
class Mod64 {
private:
  using u128 = __uint128_t;
  static constexpr u64 mul_inv(u64 n, int e=6, u64 x=1) {
    return e == 0 ? x : mul_inv(n, e-1, x*(2-x*n));
  }
public:
  static constexpr u64 inv = mul_inv(mod);
  static constexpr u64 r2 = -u128(mod) % mod;
  static constexpr int level = __builtin_ctzll(mod - 1);
  static_assert(inv * mod == 1, "invalid 1/M modulo 2^64.");

  Mod64() {}
  Mod64(u64 n) : x(init(n)) {};
  static u64 modulo() { return mod; }
  static u64 init(u64 w) { return reduce(u128(w) * r2); }
  static u64 reduce(const u128 w) { return u64(w >> 64) + mod - ((u128(u64(w) * inv) * mod) >> 64); }
  static Mod64 omega() { return Mod64(prim_root).pow((mod - 1) >> level); }
  Mod64& operator += (Mod64 rhs) { this->x += rhs.x; return *this; }
  Mod64& operator -= (Mod64 rhs) { this->x += 2 * mod - rhs.x; return *this; }
  Mod64& operator *= (Mod64 rhs) { this->x = reduce(u128(this->x) * rhs.x); return *this; }
  Mod64 operator + (Mod64 rhs) const { return Mod64(*this) += rhs; }
  Mod64 operator - (Mod64 rhs) const { return Mod64(*this) -= rhs; }
  Mod64 operator * (Mod64 rhs) const { return Mod64(*this) *= rhs; }
  u64 get() const { return reduce(this->x) % mod; }
  void set(u64 n) const { this->x = n; }
  Mod64 pow(u64 exp) const {
    Mod64 ret = Mod64(1);
    for (Mod64 base = *this; exp; exp >>= 1, base *= base) if (exp & 1) ret *= base;
    return ret;
  }
  Mod64 inverse() const { return pow(mod - 2); }
  friend ostream& operator << (ostream& os, const Mod64& m) { return os << m.get(); }
  static void Debug() {
    printf("%llu %llu %llu %llu\n", mod, inv, r2, omega().get());
  }
  u64 x;
};

template <typename mod_t>
void convolute(mod_t* A, int s1, mod_t* B, int s2, bool cyclic=false) {
  int s = (cyclic ? max(s1, s2) : s1 + s2 - 1);
  int size = 1;
  while (size < s) size <<= 1;
  mod_t roots[mod_t::level] = { mod_t::omega() };
  for(int i=1;i<mod_t::level;i++) roots[i] = roots[i - 1] * roots[i - 1];
  fill(A + s1, A + size, 0); ntt_dit4(A, size, 1, roots);
  if (A == B && s1 == s2) {
    for(int i=0;i<size;i++) A[i] *= A[i];
  } else {
    fill(B + s2, B + size, 0); ntt_dit4(B, size, 1, roots);
    for(int i=0;i<size;i++) A[i] *= B[i];
  }
  ntt_dit4(A, size, -1, roots);
  mod_t inv = mod_t(size).inverse();
  for(int i=0;i<(cyclic ? size : s);i++) A[i] *= inv;
}

template <typename mod_t>
void rev_permute(mod_t* A, int n) {
  int r = 0, nh = n >> 1;
  for(int i=1;i<n;i++) {
    for (int h = nh; !((r ^= h) & h); h >>= 1);
    if (r > i) swap(A[i], A[r]);
  }
}

template <typename mod_t>
void ntt_dit4(mod_t* A, int n, int sign, mod_t* roots) {
  rev_permute(A, n);
  int logn = __builtin_ctz(n);
  if (logn & 1) for(int i=0;i<n;i+=2) {
    mod_t a = A[i], b = A[i + 1];
    A[i] = a + b; A[i + 1] = a - b;
  }
  mod_t imag = roots[mod_t::level - 2];
  if (sign < 0) imag = imag.inverse();

  mod_t one = mod_t(1);
  for(int e=2 + (logn & 1);e<logn + 1;e+=2) {
    const int m = 1 << e;
    const int m4 = m >> 2;
    mod_t dw = roots[mod_t::level - e];
    if (sign < 0) dw = dw.inverse();

    const int block_size = max(m, (1 << 15) / int(sizeof(A[0])));
    for(int k=0;k<n;k+=block_size) {
      mod_t w = one, w2 = one, w3 = one;
      for(int j=0;j<m4;j++) {
        for(int i=k + j;i<k + block_size;i+=m) {
          mod_t a0 = A[i + m4 * 0] * one, a2 = A[i + m4 * 1] * w2;
          mod_t a1 = A[i + m4 * 2] * w,   a3 = A[i + m4 * 3] * w3;
          mod_t t02 = a0 + a2, t13 = a1 + a3;
          A[i + m4 * 0] = t02 + t13; A[i + m4 * 2] = t02 - t13;
          t02 = a0 - a2, t13 = (a1 - a3) * imag;
          A[i + m4 * 1] = t02 + t13; A[i + m4 * 3] = t02 - t13;
        }
        w *= dw; w2 = w * w; w3 = w2 * w;
      }
    }
  }
}

const int size = 1 << 17;
using m64_1 = ntt::Mod64<34703335751681, 3>;
using m64_2 = ntt::Mod64<35012573396993, 3>;
m64_1 f1[size], g1[size];
m64_2 f2[size], g2[size];

} // namespace ntt

using R = u32;
class poly {
public:
  poly() {}
  poly(int n) : coefs(n) {}
  poly(int n, int c) : coefs(n, c % mod) {}
  poly(const vector<R>& v) : coefs(v) {}
  poly(const poly& f, int beg, int end=-1) {
    if (end < 0) end = beg, beg = 0;
    resize(end - beg);
    for(int i=beg;i<end;i++) if (i < f.size()) coefs[i - beg] = f[i];
  }
  static u32 ilog2(u64 n) {
    return 63 - __builtin_clzll(n);
  }
  int size() const { return coefs.size(); }
  void resize(int s) { coefs.resize(s); }
  void push_back(R c) { coefs.push_back(c); }

  const R* data() const { return coefs.data(); }
  R* data() { return coefs.data(); }
  const R& operator [] (int i) const { return coefs[i]; }
  R& operator [] (int i) { return coefs[i]; }

  static void add(R& a, R b) { if ((a += b) >= mod) a -= mod; }
  static void sub(R& a, R b) { if (int(a -= b) < 0) a += mod; }

  poly operator - () {
    poly ret = *this;
    for(int i=0;i<(int)ret.size();i++) ret[i] = (ret[i] == 0 ? 0 : mod - ret[i]);
    return ret;
  }
  poly& operator += (const poly& rhs) {
    if (size() < rhs.size()) resize(rhs.size());
    for(int i=0;i<(int)rhs.size();i++) add(coefs[i], rhs[i]);
    return *this;
  }
  poly& operator -= (const poly& rhs) {
    if (size() < rhs.size()) resize(rhs.size());
    for(int i=0;i<(int)rhs.size();i++) sub(coefs[i], rhs[i]);
    return *this;
  }
  poly& operator *= (const poly& rhs) { return *this = *this * rhs; }

  poly operator + (const poly& rhs) const { return poly(*this) += rhs; }
  poly operator - (const poly& rhs) const { return poly(*this) -= rhs; }
  poly operator * (const poly& rhs) const { return this->mul(rhs); }

  struct fast_div {
    using u128 = __uint128_t;
    fast_div(u64 n) : m(n) {
      s = (n == 1) ? 0 : 127 - __builtin_clzll(n - 1);
      x = ((u128(1) << s) + n - 1) / n;
    }
    friend u64 operator / (u64 n, fast_div d) { return u128(n) * d.x >> d.s; }
    friend u64 operator % (u64 n, fast_div d) { return n - n / d * d.m; }
    u64 m, s, x;
  };

private:
  poly mul_crt(int beg, int end) const {
    using namespace ntt;
    auto inv = m64_2(m64_1::modulo()).inverse();
    auto fast_mod = fast_div(mod);
    auto mod1 = m64_1::modulo() % fast_mod;
    poly ret(end - beg);
    for(int i=0;i<(int)ret.size();i++) {
      u64 r1 = f1[i + beg].get(), r2 = f2[i + beg].get();
      ret[i] = (r1 + (m64_2(r2 + m64_2::modulo() - r1) * inv).get() % fast_mod * mod1) % fast_mod;
    }
    return ret;
  }

  static void mul2(const poly& f, const poly &g, bool cyclic=false) {
    using namespace ntt;
    if (&f == &g) {
      for(int i=0;i<(int)f.size();i++) f1[i] = f[i];
      convolute(f1, f.size(), f1, f.size(), cyclic);
      for(int i=0;i<(int)f.size();i++) f2[i] = f[i];
      convolute(f2, f.size(), f2, f.size(), cyclic);
    } else {
      for(int i=0;i<(int)f.size();i++) f1[i] = f[i];
      for(int i=0;i<(int)g.size();i++) g1[i] = g[i];
      convolute(f1, f.size(), g1, g.size(), cyclic);
      for(int i=0;i<(int)f.size();i++) f2[i] = f[i];
      for(int i=0;i<(int)g.size();i++) g2[i] = g[i];
      convolute(f2, f.size(), g2, g.size(), cyclic);
    }
  }

public:
  // 1.0 * M(n)
  poly mul(const poly& g) const {
    const auto& f = *this;
    if (f.size() == 0 || g.size() == 0) return poly();
    mul2(f, g, false);
    return mul_crt(0, f.size() + g.size() - 1);
  }

  // 0.5 * M(n)
  poly mul_cyclically(const poly& g) const {
    const auto& f = *this;
    if (f.size() == 0 || g.size() == 0) return poly();
    mul2(f, g, true);
    int s = max(f.size(), g.size()), size = 1;
    while (size < s) size <<= 1;
    return mul_crt(0, size);
  }

  // 1.0 * M(n)
  poly middle_product(const poly& g) const {
    const poly& f = *this;
    if (f.size() == 0 || g.size() == 0) return poly();
    mul2(f, g, true);
    return mul_crt(f.size(), g.size());
  }

  // 2.0 * M(n)
  poly inverse(int prec=-1) const {
    if (prec < 0) prec = size();
    poly ret(1, 1);
    for (int e = 1, ne; e < prec; e = ne) {
      ne = min(2 * e, prec);
      poly h = poly(ret, ne - e) * -ret.middle_product(poly(*this, ne));
      for(int i=e;i<ne;i++) ret.push_back(h[i - e]);
    }
    return ret;
  }

  // 2.5 * M(n)
  poly quotient(const poly& b) const {
    assert(size() == b.size());
    int s = size() / 2 + 1;
    poly inv = b.inverse(s);
    poly q1 = poly(poly(*this, s) * inv, s);
    poly lo = q1.middle_product(b);
    poly q2 = poly(inv, size() - s) * (poly(*this, s, size()) - lo);
    for(int i=0;i<size() - s;i++) q1.push_back(q2[i]);
    return q1;
  }

  // 0.5 * M(n) : f - q * d
  static poly sub_mul(const poly& f, const poly& q, const poly& d) {
    int sq = q.size();
    poly p = q.mul_cyclically(d);
    int mask = p.size() - 1;
    for(int i=0;i<sq;i++) sub(p[i & mask], f[i & mask]);
    poly r = poly(f, sq, f.size());
    for(int i=0;i<(int)r.size();i++) sub(r[i], p[(sq + i) & mask]);
    return r;
  }

  // 3.0 * M(n)
  pair<poly, poly> divrem(const poly& b) const {
    if (size() < b.size()) return make_pair(poly(), poly(*this));
    assert(size() < 2 * b.size());
    int sq = size() - b.size() + 1;
    poly q = poly(*this, sq).quotient(poly(b, sq));
    poly r = sub_mul(*this, q, b);
    return make_pair(q, r);
  }

  // 3.0 * M(n)
  poly rem(const poly& b) const {
    return divrem(b).second;
  }

  // 1.5 * M(n)
  pair<poly, poly> divrem_pre(const poly& b, const poly& inv) const {
    if (size() < b.size()) return make_pair(poly(), poly(*this));
    int sq = size() - b.size() + 1;
    assert(size() >= sq && inv.size() >= sq);
    poly q = poly(poly(*this, sq) * poly(inv, sq), sq);
    poly r = sub_mul(*this, q, b);
    return make_pair(q, r);
  }

  // 1.5 * M(n)
  poly rem_pre(const poly& f, const poly& inv) const {
    return divrem_pre(f, inv).second;
  }

  // 13/6 * M(n) * log2_(e) : x^e (mod f)
  static poly x_pow_mod(u64 e, const poly& f) {
    if (e == 0) return poly(1, 1);
    poly ret = poly(vector<R>({1, 0}));
    poly inv = f.inverse(f.size());
    ret = ret.rem_pre(f, inv);
    u64 mask = (u64(1) << ilog2(e)) >> 1;
    while (mask) {
      ret *= ret;
      if (e & mask) ret.push_back(0);
      ret = ret.rem_pre(f, inv);
      mask >>= 1;
    }
    return ret;
  }

public:
  vector<R> coefs;
  static R mod;
};
R poly::mod;


double tick() {
  static clock_t oldtick;
  clock_t newtick = clock();
  double diff = 1.0*(newtick - oldtick) / CLOCKS_PER_SEC;
  oldtick = newtick;
  return diff;
}

signed main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  //tick();
  poly::mod=MOD;
  ll K;cin>>K;
  ll N;cin>>N;
  poly f(1<<17,0);
  for(ll i=0;i<N;i++){
    ll x;cin>>x;
    f[x]=MOD-1;
  }
  f[0]=1;
  //cerr<<"???"<<endl;
  auto g=f.inverse();
  //cerr<<"!!!"<<endl;
  cout<<g[K]<<endl;
  //cerr<<tick()<<endl;
  return 0;
}