Submission #66163552

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Source Code Expand

#pragma GCC optimize("O3")
#include "bits/stdc++.h"
using namespace std;
#define all(x) x.begin(),x.end()
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) { return os << p.first << " " << p.second; }
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type> ostream& operator<<(ostream &os, const T_container &v) { string sep; for (const T &x : v) os << sep << x, sep = " "; return os; }
#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) 42
#define ASSERT(...) 42
#endif
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int,int> pi;
const int oo = 1e9;
const long long MD = 998244353;
template<long long MOD=MD> struct mdint {
    int d;
    mdint () {d=0;}
    mdint (long long _d) : d(_d%MOD){
        if(d<0) d+=MOD;
    };
    friend mdint& operator+=(mdint& a, const mdint& o) {
        a.d+=o.d; if(a.d>=MOD) a.d-=MOD;
        return a;
    }
    friend mdint& operator-=(mdint& a, const mdint& o) {
        a.d-=o.d; if(a.d<0) a.d+=MOD;
        return a;
    }
    friend mdint& operator*=(mdint& a, const mdint& o) {
        return a = mdint((ll)a.d*o.d);
    }
    mdint operator*(const mdint& o) const {
        mdint res = *this;
        res*=o;
        return res;
    }
    mdint operator+(const mdint& o) const {
        mdint res = *this;
        res+=o;
        return res;
    }
    mdint operator-(const mdint& o) const {
        mdint res = *this;
        res-=o;
        return res;
    }
    mdint operator^(long long b) const {
        mdint tmp = 1;
        mdint power = *this;
        while(b) {
            if(b&1) {
                tmp = tmp*power;
            }
            power = power*power;
            b/=2;
        }
        return tmp;
    }
    friend mdint operator/=(mdint& a, const mdint& o) {
        a *= (o^(MOD-2));
        return a;
    }
    mdint operator/(const mdint& o) {
        mdint res = *this;
        res/=o;
        return res;
    }
    auto operator<=>(const mdint& o) const { return d<=>o.d;}
    friend istream& operator>>(istream& c, mdint& a) {return c >> a.d;}
    friend ostream& operator<<(ostream& c, const mdint& a) {return c << a.d;}
};
using  mint = mdint<MD>;
void fft(auto a, auto b) {
    int n = b-a;
    for(int j=0;(1<<j)<n;++j) for(int i=0;i<n;++i) if(1<<j & i) {
        a[i]+=a[i^(1<<j)];
    }
    
}
void ifft(auto a,auto b) {
    int n = b-a;
    for(int j=0;(1<<j)<n;++j) for(int i=0;i<n;++i) if(1<<j & i) {
        a[i]-=a[i^(1<<j)];
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int n,m; cin >> n >> m;
    const int K = 1<<n;
    vi a(K);
    for(int i=0;i<m;++i) {
        int x; cin >> x;
        a[x]++;
    }
    fft(all(a));
    vector<mint> dp(K+1);
    // want to keep prefix sum updated.
    // when a bit disappears:
    // 
    dp[0]=1;
    vector<mint> cur(K);
    auto solve = [&](auto&& self, int l, int r, auto L, auto R) -> void {
        if(r-l==1) {
            dp[l+1] += dp[l] * L[0];
            return;
        }
        int mid = (l+r)/2;
        int len = r-l;
        self(self,l,mid,L, L+len/2);
        // transition!

        {
        copy(dp.begin()+l,dp.begin()+mid,cur.begin());
        fft(cur.begin(),cur.begin()+len/2);
        for(int i=0;i<len/2;++i) cur[i]*=(L[i+len/2]-L[i]);
        ifft(cur.begin(),cur.begin()+len/2);

        for(int i=0;i<len/2;++i) {
            dp[mid+i+1]+=cur[i];
        }
        }


        self(self,mid,r,L+len/2,R);

    };
    solve(solve,0,K,all(a));
    cout << dp[K] << '\n';
}

Submission Info

Judge Result