Problem p03406 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#define _USE_MATH_DEFINES
#include <complex>
#include <functional>
#include <math.h>
using namespace std;

#define rep(i, x) for (ll i = 0; i < x; i++)
#define repn(i, x) for (ll i = 1; i <= x; i++)

typedef long long ll;
const ll INF = 1e17;
const ll MOD = 1000000007;
const ll MAX = 4000001;
const long double eps = 1E-14;

ll max(ll a, ll b) {
  if (a > b) {
    return a;
  }
  return b;
}

ll min(ll a, ll b) {
  if (a > b) {
    return b;
  }
  return a;
}

ll gcd(ll a, ll b) {
  if (b == 0) {
    return a;
  }
  if (a < b) {
    return gcd(b, a);
  }
  return gcd(b, a % b);
}

ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

struct edge {
  ll ind;
  ll fr;
  ll to;
  ll d;
};

class mint {
  long long x;

public:
  mint(long long x = 0) : x((x % MOD + MOD) % MOD) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint &a) {
    if ((x += a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator-=(const mint &a) {
    if ((x += MOD - a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator*=(const mint &a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator+(const mint &a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint &a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint &a) const {
    mint res(*this);
    return res *= a;
  }

  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime MOD
  mint inv() const { return pow(MOD - 2); }
  mint &operator/=(const mint &a) { return (*this) *= a.inv(); }
  mint operator/(const mint &a) const {
    mint res(*this);
    return res /= a;
  }

  friend ostream &operator<<(ostream &os, const mint &m) {
    os << m.x;
    return os;
  }
};

mint pw(mint a, ll b) {
  if (b == 0) {
    return 1;
  }
  mint ret = pw(a, b >> 1);
  ret *= ret;
  if (b & 1) {
    ret *= a;
  }
  return ret;
}

typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<vector<vector<ll>>> vvvll;

typedef vector<mint> vmint;
typedef vector<vector<mint>> vvmint;
typedef vector<vector<vector<mint>>> vvvmint;

//////////////////////////////////////
vmint f, finv, inv;

void cominit(ll N) {
  f.assign(N + 1, 1);
  finv.assign(N + 1, 1);
  inv.assign(N + 1, 1);
  inv[1] = 1;

  repn(i, N) {
    f[i] = f[i - 1] * i;
    if (i > 1)
      inv[i] = -inv[MOD % i] * (MOD / i);
    finv[i] = finv[i - 1] * inv[i];
  }
}

mint per(ll a, ll b) {
  if (a < 0 || b < 0 || a < b) {
    return 0;
  }
  return f[a] * finv[a - b];
}

int main() {
  ll N, M;
  cin >> N >> M;

  cominit(1 << (N + 1));

  vll A(M + 2, 0);
  A[0] = 1;
  repn(i, M) cin >> A[i];
  A[M + 1] = (1 << N) + 1;

  vvmint dp(M + 2, vmint(1 << N, 0));

  dp[0][0] = 1;

  repn(i, M + 1) {
    rep(j, 1 << N) {
      for (ll k = j; k >= 0; k = j & (k - 1)) {

        dp[i][j] += dp[i - 1][k] * per(j - (A[i - 1] - 1), A[i] - A[i - 1] - 1);

        if (k != j)
          dp[i][j] -= dp[i][k];

        if (k == 0) {
          break;
        }
      }

      // cout << i << " " << j << " " << dp[i][j] << endl;
    }

    if (i <= M) {
      rep(j, 1 << N) {
        dp[i][j] *= (j - (A[i] - 2));
        // cout << i << " " << j << " " << dp[i][j] << endl;
      }
    }
  }

  mint ans = dp[M + 1][(1 << N) - 1];
  ans *= (1 << N);

  cout << ans << endl;
}


Fixed submission:
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#define _USE_MATH_DEFINES
#include <complex>
#include <functional>
#include <math.h>
using namespace std;

#define rep(i, x) for (ll i = 0; i < x; i++)
#define repn(i, x) for (ll i = 1; i <= x; i++)

typedef long long ll;
const ll INF = 1e17;
const ll MOD = 1000000007;
const ll MAX = 4000001;
const long double eps = 1E-14;

ll max(ll a, ll b) {
  if (a > b) {
    return a;
  }
  return b;
}

ll min(ll a, ll b) {
  if (a > b) {
    return b;
  }
  return a;
}

ll gcd(ll a, ll b) {
  if (b == 0) {
    return a;
  }
  if (a < b) {
    return gcd(b, a);
  }
  return gcd(b, a % b);
}

ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

struct edge {
  ll ind;
  ll fr;
  ll to;
  ll d;
};

class mint {
  long long x;

public:
  mint(long long x = 0) : x((x % MOD + MOD) % MOD) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint &a) {
    if ((x += a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator-=(const mint &a) {
    if ((x += MOD - a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator*=(const mint &a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator+(const mint &a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint &a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint &a) const {
    mint res(*this);
    return res *= a;
  }

  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime MOD
  mint inv() const { return pow(MOD - 2); }
  mint &operator/=(const mint &a) { return (*this) *= a.inv(); }
  mint operator/(const mint &a) const {
    mint res(*this);
    return res /= a;
  }

  friend ostream &operator<<(ostream &os, const mint &m) {
    os << m.x;
    return os;
  }
};

mint pw(mint a, ll b) {
  if (b == 0) {
    return 1;
  }
  mint ret = pw(a, b >> 1);
  ret *= ret;
  if (b & 1) {
    ret *= a;
  }
  return ret;
}

typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<vector<vector<ll>>> vvvll;

typedef vector<mint> vmint;
typedef vector<vector<mint>> vvmint;
typedef vector<vector<vector<mint>>> vvvmint;

//////////////////////////////////////
vmint f, finv, inv;

void cominit(ll N) {
  f.assign(N + 1, 1);
  finv.assign(N + 1, 1);
  inv.assign(N + 1, 1);
  inv[1] = 1;

  repn(i, N) {
    f[i] = f[i - 1] * i;
    if (i > 1)
      inv[i] = -inv[MOD % i] * (MOD / i);
    finv[i] = finv[i - 1] * inv[i];
  }
}

mint per(ll a, ll b) {
  if (a < 0 || b < 0 || a < b) {
    return 0;
  }
  return f[a] * finv[a - b];
}

int main() {
  ll N, M;
  cin >> N >> M;

  cominit(1 << (N + 1));

  vll A(M + 2, 0);
  A[0] = 1;
  repn(i, M) cin >> A[i];
  A[M + 1] = (1 << N) + 1;

  vvmint dp(M + 2, vmint(1 << N, 0));

  dp[0][0] = 1;

  repn(i, M + 1) {

    vmint rdp(1 << N, 0);
    rep(s, 1 << N) rdp[s] = dp[i - 1][s];

    rep(k, N) rep(s, 1 << N) {
      if ((s >> k) & 1)
        rdp[s] += rdp[s ^ (1 << k)];
    }

    rep(j, 1 << N) { rdp[j] *= per(j - (A[i - 1] - 1), A[i] - A[i - 1] - 1); }

    rep(s, 1 << N) dp[i][s] = rdp[s];

    rep(k, N) rep(s, 1 << N) {
      if ((s >> k) & 1)
        dp[i][s] -= dp[i][s ^ (1 << k)];
    }

    if (i <= M) {
      rep(j, 1 << N) {
        dp[i][j] *= (j - (A[i] - 2));
        // cout << i << " " << j << " " << dp[i][j] << endl;
      }
    }
  }

  mint ans = dp[M + 1][(1 << N) - 1];
  ans *= (1 << N);

  cout << ans << endl;
}