Language: C++

#include <iostream>
#include <vector>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <algorithm>
#include <cassert>
#define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define pb push_back
using namespace std;
using ll = std::int_fast64_t;
using P = pair<ll, ll>;
constexpr ll inf = 1000000000;
constexpr ll mod = 1000000007;
constexpr long double eps = 1e-15;
 
template<typename T1, typename T2>
ostream& operator<<(ostream& os, pair<T1, T2> p) {
    os << to_string(p.first) << " " << to_string(p.second);
    return os;
}
template<typename T>
ostream& operator<<(ostream& os, vector<T>& v) {
    REP(i, v.size()) {
        if(i) os << " ";
        os << to_string(v[i]);
    }
    return os;
}
 
struct modint {
    ll n;
public:
    modint(const ll n = 0) : n((n % mod + mod) % mod) {}
    static modint pow(modint a, int m) {
        modint r = 1;
        while(m > 0) {
            if(m & 1) { r *= a; }
            a = (a * a); m /= 2;
        }
        return r;
    }
    modint &operator++() { *this += 1; return *this; }
    modint &operator--() { *this -= 1; return *this; }
    modint operator++(int) { modint ret = *this; *this += 1; return ret; }
    modint operator--(int) { modint ret = *this; *this -= 1; return ret; }
    modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
    friend bool operator==(const modint& lhs, const modint& rhs) {
        return lhs.n == rhs.n;
    }
    friend bool operator<(const modint& lhs, const modint& rhs) {
        return lhs.n < rhs.n;
    }
    friend bool operator>(const modint& lhs, const modint& rhs) {
        return lhs.n > rhs.n;
    }
    friend modint &operator+=(modint& lhs, const modint& rhs) {
        lhs.n += rhs.n;
        if (lhs.n >= mod) lhs.n -= mod;
        return lhs;
    }
    friend modint &operator-=(modint& lhs, const modint& rhs) {
        lhs.n -= rhs.n;
        if (lhs.n < 0) lhs.n += mod;
        return lhs;
    }
    friend modint &operator*=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * rhs.n) % mod;
        return lhs;
    }
    friend modint &operator/=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * (~rhs).n) % mod;
        return lhs;
    }
    friend modint operator+(const modint& lhs, const modint& rhs) {
        return modint(lhs.n + rhs.n);
    }
    friend modint operator-(const modint& lhs, const modint& rhs) {
        return modint(lhs.n - rhs.n);
    }
    friend modint operator*(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * rhs.n);
    }
    friend modint operator/(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * (~rhs).n);
    }
};
istream& operator>>(istream& is, modint m) { is >> m.n; return is; }
ostream& operator<<(ostream& os, modint m) { os << m.n; return os; }
 
#define MAX_N 3030303
long long extgcd(long long a, long long b, long long& x, long long& y) {
    long long d = a;
    if (b != 0) {
        d = extgcd(b, a % b, y, x);
        y -= (a / b) * x;
    } else {
        x = 1; y = 0;
    }
    return d;
}
long long mod_inverse(long long a, long long m) {
    long long x, y;
    if(extgcd(a, m, x, y) == 1) return (m + x % m) % m;
    else return -1;
}
vector<long long> fact(MAX_N+1, inf);
long long mod_fact(long long n, long long& e) {
    if(fact[0] == inf) {
        fact[0]=1;
        if(MAX_N != 0) fact[1]=1;
        for(ll i = 2; i <= MAX_N; ++i) {
            fact[i] = (fact[i-1] * i) % mod;
        }
    }
    e = 0;
    if(n == 0) return 1;
    long long res = mod_fact(n / mod, e);
    e += n / mod;
    if((n / mod) % 2 != 0) return (res * (mod - fact[n % mod])) % mod;
    return (res * fact[n % mod]) % mod;
}
// return nCk
long long mod_comb(long long n, long long k) {
    if(n < 0 || k < 0 || n < k) return 0;
    long long e1, e2, e3;
    long long a1 = mod_fact(n, e1), a2 = mod_fact(k, e2), a3 = mod_fact(n - k, e3);
    if(e1 > e2 + e3) return 0;
    return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod;
}
 
using mi = modint;
 
mi mod_pow(mi a, ll n) {
    mi ret = 1;
    mi tmp = a;
    while(n > 0) {
        if(n % 2) ret *= tmp;
        tmp = tmp * tmp;
        n /= 2;
    }
    return ret;
}

vector<mi> f(100000, 1), invf(100000, 1);

void init() {
    FOR(i, 1, 100000) f[i] = f[i - 1] * i;
    invf[99999] = mod_pow(f[99999], mod - 2);
    for(int i = 99999 - 1; i > 0; i--) invf[i] = invf[i + 1] * (i + 1);
    return;
}

mi comb(int n, int k) {
    assert(n >= 0 && k >= 0 && n >= k);
    return f[n] * invf[k] * invf[n - k];
}

mi dp[16][(1 << 16)];

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    init();
    int n, m;
    cin >> n >> m;
    int nn = (1 << n);
    vector<int> a(m);
    REP(i, m) cin >> a[i];
    mi co = nn;
    REP(i, n) REP(j, (1 << i)) co *= (j + 1);
    mi ans = 1;
    int sum = 0;
    REP(j, n) {
        ans *= comb(nn - 1 - sum, (1 << j));
        sum += (1 << j);
    }
    for(int i = m - 1; i >= 0; i--) for(int j = 1; j < nn; j++) {
        bitset<16> b(j);
        if((int)b.count() > m - i || b.to_ullong() > nn - a[i] + 1) continue;
        if((int)b.count() == 1) {
            dp[i][j] = comb(nn - a[i], b.to_ullong() - 1);
        } else {
            REP(k, n) {
                if(!b[k]) continue;
                b[k] = 0;
                for(int l = i + 1; l < m; l++) {
                    dp[i][j] += dp[l][b.to_ullong()] * comb(nn - a[i] - b.to_ullong(), (1 << k) - 1);
                }
                b[k] = 1;
            }
        }
        mi co2 = 1;
        int sum = 0;
        REP(k, n) {
            if(b[k]) continue;
            co2 *= comb(nn - 1 - b.to_ullong() - sum, (1 << k));
            sum += (1 << k);
        }
        if(b.count() % 2) ans -= co2 * dp[i][j];
        else ans += co2 * dp[i][j];
    }
    cout << co * ans << endl;
    return 0;
}


Compiler output:
a.cc:14:17: error: 'int_fast64_t' in namespace 'std' does not name a type
   14 | using ll = std::int_fast64_t;
      |                 ^~~~~~~~~~~~
a.cc:15:16: error: 'll' was not declared in this scope
   15 | using P = pair<ll, ll>;
      |                ^~
a.cc:15:20: error: 'll' was not declared in this scope
   15 | using P = pair<ll, ll>;
      |                    ^~
a.cc:15:22: error: template argument 1 is invalid
   15 | using P = pair<ll, ll>;
      |                      ^
a.cc:15:22: error: template argument 2 is invalid
a.cc:16:11: error: 'll' does not name a type
   16 | constexpr ll inf = 1000000000;
      |           ^~
a.cc:17:11: error: 'll' does not name a type
   17 | constexpr ll mod = 1000000007;
      |           ^~
a.cc: In function 'std::ostream& operator<<(std::ostream&, std::vector<_Tp>&)':
a.cc:9:26: error: 'll' was not declared in this scope
    9 | #define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
      |                          ^~
a.cc:10:19: note: in expansion of macro 'FOR'
   10 | #define REP(i, n) FOR(i, 0, n)
      |                   ^~~
a.cc:27:5: note: in expansion of macro 'REP'
   27 |     REP(i, v.size()) {
      |     ^~~
a.cc:27:9: error: 'i' was not declared in this scope
   27 |     REP(i, v.size()) {
      |         ^
a.cc:9:36: note: in definition of macro 'FOR'
    9 | #define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
      |                                    ^
a.cc:27:5: note: in expansion of macro 'REP'
   27 |     REP(i, v.size()) {
      |     ^~~
a.cc: At global scope:
a.cc:35:5: error: 'll' does not name a type
   35 |     ll n;
      |     ^~
a.cc:37:18: error: 'll' does not name a type
   37 |     modint(const ll n = 0) : n((n % mod + mod) % mod) {}
      |                  ^~
a.cc: In constructor 'modint::modint(int)':
a.cc:37:30: error: class 'modint' does not have any field named 'n'
   37 |     modint(const ll n = 0) : n((n % mod + mod) % mod) {}
      |                              ^
a.cc:37:37: error: 'mod' was not declared in this scope
   37 |     modint(const ll n = 0) : n((n % mod + mod) % mod) {}
      |                                     ^~~
a.cc: In member function 'modint modint::operator~() const':
a.cc:50:52: error: 'n' was not declared in this scope
   50 |     modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
      |                                                    ^
a.cc:50:55: error: 'mod' was not declared in this scope
   50 |     modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
      |                                                       ^~~
a.cc: In function 'bool operator==(const modint&, const modint&)':
a.cc:52:20: error: 'const struct modint' has no member named 'n'
   52 |         return lhs.n == rhs.n;
      |                    ^
a.cc:52:29: error: 'const struct modint' has no member named 'n'
   52 |         return lhs.n == rhs.n;
      |                             ^
a.cc: In function 'bool operator<(const modint&, const modint&)':
a.cc:55:20: error: 'const struct modint' has no member named 'n'
   55 |         return lhs.n < rhs.n;
      |                    ^
a.cc:55:28: error: 'const struct modint' has no member named 'n'
   55 |         return lhs.n < rhs.n;
      |                            ^
a.cc: In function 'bool operator>(const modint&, const modint&)':
a.cc:58:20: error: 'const struct modint' has no member named 'n'
   58 |         return lhs.n > rhs.n;
      |                    ^
a.cc:58:28: error: 'const struct modint' has no member named 'n'
   58 |         return lhs.n > rhs.n;
      |                            ^
a.cc: In function 'modint& operator+=(modint&, const modint&)':
a.cc:61:13: error: 'struct modint' has no member named 'n'
   61 |         lhs.n += rhs.n;
      |             ^
a.cc:61:22: error: 'const struct modint' has no member named 'n'
   61 |         lhs.n += rhs.n;
      |                      ^
a.cc:62:17: error: 'struct modint' has no member named 'n'
   62 |         if (lhs.n >= mod) lhs.n -= mod;
      |                 ^
a.cc:62:22: error: 'mod' was not declared in this scope
   62 |         if (lhs.n >= mod) lhs.n -= mod;
      |                      ^~~
a.cc:62:31: error: 'struct modint' has no member named 'n'
   62 |         if (lhs.n >= mod) lhs.n -= mod;
      |                               ^
a.cc: In function 'modint& operator-=(modint&, const modint&)':
a.cc:66:13: error: 'struct modint' has no member named 'n'
   66 |         lhs.n -= rhs.n;
      |             ^
a.cc:66:22: error: 'const struct modint' has no member named 'n'
   66 |         lhs.n -= rhs.n;
      |                      ^
a.cc:67:17: error: 'struct modint' has no member named 'n'
   67 |         if (lhs.n < 0) lhs.n += mod;
      |                 ^
a.cc:67:28: error: 'struct modint' has no member named 'n'
   67 |         if (lhs.n < 0) lhs.n += mod;
      |                            ^
a.cc:67:33: error: 'mod' was not declared in this scope
   67 |         if (lhs.n < 0) lhs.n += mod;
      |                                 ^~~
a.cc: In function 'modint& operator*=(modint&, const modint&)':
a.cc:71:13: error: 'struct modint' has no member named 'n'
   71 |         lhs.n = (lhs.n * rhs.n) % mod;
      |             ^
a.cc:71:22: error: 'struct modint' has no member named 'n'
   71 |         lhs.n = (lhs.n * rhs.n) % mod;
      |                      ^
a.cc:71:30: error: 'const struct modint' has no member named 'n'
   71 |         lhs.n = (lhs.n * rhs.n) % mod;
      |                              ^
a.cc:71:35: error: 'mod' was not declared in this scope
   71 |         lhs.n = (lhs.n * rhs.n) % mod;
      |                                   ^~~
a.cc: In function 'modint& operator/=(modint&, const modint&)':
a.cc:75:13: error: 'struct modint' has no member named 'n'
   75 |         lhs.n = (lhs.n * (~rhs).n) % mod;
      |             ^
a.cc:75:22: error: 'struct modint' has no member named 'n'
   75 |         lhs.n = (lhs.n * (~rhs).n) % mod;
      |                      ^
a.cc:75:33: error: 'struct modint' has no member named 'n'
   75 |         lhs.n = (lhs.n * (~rhs).n) % mod;
      |                                 ^
a.cc:75:38: error: 'mod' was not declared in this scope
   75 |         lhs.n = (lhs.n * (~rhs).n) % mod;
      |                                      ^~~
a.cc: In function 'modint operator+(const modint&, const modint&)':
a.cc:79:27: error: 'const struct modint' has no member named 'n'
   79 |         return modint(lhs.n + rhs.n);
      |                           ^
a.cc:79:35: error: 'const struct modint' has no member named 'n'
   79 |         return modint(lhs.n + rhs.n);
      |                                   ^
a.cc: In function 'modint operator-(const modint&, const modint&)':
a.cc:82:27: error: 'const struct modint' has no member named 'n'
   82 |         return modint(lhs.n - rhs.n);
      |                           ^
a.cc:82:35: error: 'const struct modint' has no member named 'n'
   82 |         return modint(lhs.n - rhs.n);
      |                                   ^
a.cc: In function 'modint operator*(const modint&, const modint&)':
a.cc:85:27: error: 'const struct modint' has no member named 'n'
   85 |         return modint(lhs.n * rhs.n);
      |                           ^
a.cc:85:35: error: 'const struct modint' has no member named 'n'
   85 |         return modint(lhs.n * rhs.n);
      |                                   ^
a.cc: In function 'modint operator/(const modint&, const modint&)':
a.cc:88:27: error: 'const struct modint' has no member named 'n'
   88 |         return modint(lhs.n * (~rhs).n);
      |                           ^
a.cc:88:38: error: 'struct modint' has no member named 'n'
   88 |         return modint(lhs.n * (~rhs).n);
      |                                      ^
a.cc: In function 'std::istream& operator>>(std::istream&, modint)':
a.cc:91:54: error: 'struct modint' has no member named 'n'
   91 | istream& operator>>(istream& is, modint m) { is >> m.n; return is; }
      |                                                      ^
a.cc: In function 'std::ostream& operator<<(std::ostream&, modint)':
a.cc:92:54: error: 'struct modint' has no member named 'n'
   92 | ostream& operator<<(ostream& os, modint m) { os << m.n; return os; }
      |                                                      ^
a.cc: At global scope:
a.cc:110:33: error: 'inf' was not declared in this scope; did you mean 'int'?
  110 | vector<long long> fact(MAX_N+1, inf);
      |                                 ^~~
      |                                 int
a.cc: In function 'long long int mod_fact(long long int, long long int&)':
a.cc:112:19: error: 'inf' was not declared in this scope; did you mean 'int'?
  112 |     if(fact[0] == inf) {
      |                   ^~~
      |                   int
a.cc:115:13: error: 'll' was not declared in this scope
  115 |         for(ll i = 2; i <= MAX_N; ++i) {
      |             ^~
a.cc:115:23: error: 'i' was not declared in this scope
  115 |         for(ll i = 2; i <= MAX_N; ++i) {
      |                       ^
a.cc:116:41: error: 'mod' was not declared in this scope
  116 |             fact[i] = (fact[i-1] * i) % mod;
      |                                         ^~~
a.cc:121:34: error: 'mod' was not declared in this scope
  121 |     long long res = mod_fact(n / mod, e);
      |                                  ^~~
a.cc: In function 'long long int mod_comb(long long int, long long int)':
a.cc:132:42: error: 'mod' was not declared in this scope
  132 |     return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod;
      |                                          ^~~
a.cc: At global scope:
a.cc:137:18: error: 'll' has not been declared
  137 | mi mod_pow(mi a, ll n) {
      |                  ^~
a.cc: In function 'void init()':
a.cc:9:26: error: 'll' was not declared in this scope
    9 | #define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
      |                          ^~
a.cc:151:5: note: in expansion of macro 'FOR'
  151 |     FOR(i, 1, 100000) f[i] = f[i - 1] * i;
      |     ^~~
a.cc:151:9: error: 'i' was not declared in this scope; did you mean 'mi'?
  151 |     FOR(i, 1, 100000) f[i] = f[i - 1] * i;