#133688 (C++11（廃止可能性あり）) No.462 6日知らずのコンピュータ

• 問題: No.462 6日知らずのコンピュータ
• ユーザー: はむこ
• 提出日時: 2016-11-29 10:41:40
• 言語: C++11（廃止可能性あり） (gcc 13.3.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 6,654 bytes
• コンパイル時間: 2,382 ms
• コンパイル使用メモリ: 177,428 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-11-29 17:58:10
• 合計ジャッジ時間: 3,988 ms
• ジャッジサーバーID （参考情報）: judge3 / judge1

ファイルパターン	結果
sample	AC * 3
other	AC * 84

ソースコード

#include <bits/stdc++.h>
using namespace std;

#ifdef _WIN32
#define scanfll(x) scanf("%I64d", x)
#define printfll(x) printf("%I64d", x)
#else
#define scanfll(x) scanf("%lld", x)
#define printfll(x) printf("%lld", x)
#endif
#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

using ll = long long; using vll = vector<ll>; using vvll = vector<vll>;
using ld = long double;  using vld = vector<ld>; 
using vi = vector<int>; using vvi = vector<vi>;
vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; }
using P = pair<ll, ll>;

template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) {  o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args> 
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; cout << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const unordered_map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]";  return o; }
string bits_to_string(ll mask, ll n) { string s; rep(i, n) s += '0' + !!(mask & (1ll << i)); return s; }
#define ldout fixed << setprecision(40) 

static const double EPS = 1e-14;
static const long long INF = 1e18;

static const long long mo = 1e9+7;
class Mod {
    public:
        int num;
        Mod() : Mod(0) {}
        Mod(long long int n) : num(n) { }
        Mod(const string &s){ long long int tmp = 0; for(auto &c:s) tmp = (c-'0'+tmp*10) % mo; num = tmp; }
        Mod(int n) : Mod(static_cast<long long int>(n)) {}
        operator int() { return num; }
};
istream &operator>>(istream &is, Mod &x) { long long int n; is >> n; x = n; return is; }
ostream &operator<<(ostream &o, const Mod &x) { o << x.num; return o; }
Mod operator+(const Mod a, const Mod b) { return Mod((a.num + b.num) % mo); }
Mod operator+(const long long int a, const Mod b) { return Mod(a) + b; }
Mod operator+(const Mod a, const long long int b) { return b + a; }
Mod operator++(Mod &a) { return a + Mod(1); }
Mod operator-(const Mod a, const Mod b) { return Mod((mo + a.num - b.num) % mo); }
Mod operator-(const long long int a, const Mod b) { return Mod(a) - b; }
Mod operator--(Mod &a) { return a - Mod(1); }
Mod operator*(const Mod a, const Mod b) { return Mod(((long long)a.num * b.num) % mo); }
Mod operator*(const long long int a, const Mod b) { return Mod(a)*b; }
Mod operator*(const Mod a, const long long int b) { return Mod(b)*a; }
Mod operator*(const Mod a, const int b) { return Mod(b)*a; }
Mod operator+=(Mod &a, const Mod b) { return a = a + b; }
Mod operator+=(long long int &a, const Mod b) { return a = a + b; }
Mod operator-=(Mod &a, const Mod b) { return a = a - b; }
Mod operator-=(long long int &a, const Mod b) { return a = a - b; }
Mod operator*=(Mod &a, const Mod b) { return a = a * b; }
Mod operator*=(long long int &a, const Mod b) { return a = a * b; }
Mod operator*=(Mod& a, const long long int &b) { return a = a * b; }
Mod factorial(const long long n) {
    if (n < 0) return 0;
    Mod ret = 1;
    for (int i = 1; i <= n; i++) {
        ret *= i;
    }
    return ret;
}
Mod operator^(const Mod a, const long long n) {
    if (n == 0) return Mod(1);
    Mod res = (a * a) ^ (n / 2);
    if (n % 2) res = res * a;
    return res;
}
Mod modpowsum(const Mod a, const long long b) {
    if (b == 0) return 0;
    if (b % 2 == 1) return modpowsum(a, b - 1) * a + Mod(1);
    Mod result = modpowsum(a, b / 2);
    return result * (a ^ (b / 2)) + result;
}


/*************************************/
// 以下、modは素数でなくてはならない！
/*************************************/
Mod inv(const Mod a) { return a ^ (mo - 2); }
Mod operator/(const Mod a, const Mod b) { assert(b.num != 0); return a * inv(b); }
Mod operator/(const long long int a, const Mod b) { assert(b.num != 0); return Mod(a) * inv(b); }
Mod operator/=(Mod &a, const Mod b) { assert(b.num != 0); return a = a * inv(b); }

// n!と1/n!のテーブルを作る。
// nCrを高速に計算するためのもの。
//
// assertでnを超えていないかをきちんとテストすること。
//
// O(n log mo)
vector<Mod> fact, rfact;
void constructFactorial(const long long n) {
    fact.resize(n);
    rfact.resize(n);
    fact[0] = rfact[0] = 1;
    for (int i = 1; i < n; i++) {
        fact[i] = fact[i-1] * i;
        rfact[i] = Mod(1) / fact[i];
    }
}

int main(void) {
    cin.tie(0); ios::sync_with_stdio(false);
    constructFactorial(100);
    ll n, k; cin >> n >> k;

    vll a(k); rep(i, a.size()) cin >> a[i];
    sort(all(a));
    rep(i, k-1) {
        rep(bit, 61) {
            if ((a[i]&(1ll<<bit)) && !(a[i+1]&(1ll<<bit))) {
                cout << 0 << endl;
                return 0;
            }
        }
    }

    set<ll> popc;
    popc.insert(0);
    popc.insert(n);
    rep(i, k) {
        popc.insert(__builtin_popcountll(a[i]));
    }
    vll b; for (auto x : popc)  b.pb(x);

    Mod ret = 1;
    rep(i, b.size()-1) {
        ret *= fact[b[i+1] - b[i]];
    }
    cout << ret << endl;
    return 0;
}