Submission #9537437

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Source Code Expand

#include <bits/stdc++.h>
#define meow(args...) fprintf(stderr, args)
inline bool cmin(auto &a, const auto &b) {return b<a?(a=b, true):false;}
inline bool cmax(auto &a, const auto &b) {return a<b?(a=b, true):false;}
template<class Type> Type read() {
	Type a;
	bool b;
	unsigned char c;
	while(c=getchar()-48, (c>9)&(c!=253));
	for(a=(b=c==253)?0:c; (c=getchar()-48)<=9; a=a*10+c);
	return b?-a:a;
}
auto rd=read<int>;
typedef unsigned u32;
typedef long long s64;
typedef unsigned long long u64;
const u32 P=1e9+7;
u32 &inc(u32 &a, u32 b) {return (a+=b)<P?a:(a-=P);}
u32 &dec(u32 &a, u32 b) {return (a-=b)&0x80000000?(a+=P):a;}
u32 sum(u32 a, u32 b) {return inc(a, b);}
u32 dif(u32 a, u32 b) {return dec(a, b);}
u64 power(u64 a, int b) {
	u64 ans=1;
	for(; b; a=a*a%P, b/=2) if(b&1) ans=ans*a%P;
	return ans;
}

const int T=65555;
int a[16];
u32 fac[T], ifac[T], f[T];
u64 arr(int n, int r) {return n<0||r<0||r>n?0:(u64)fac[n]*ifac[n-r]%P;}
int main() {
	int n=rd(), m=rd(), tot=1<<n;
	u32 ans=0;
	std::generate(a, a+m, rd);
	fac[0]=1;
	for(int i=1; i<=tot; ++i) fac[i]=(u64)fac[i-1]*i%P;
	ifac[tot]=power(fac[tot], P-2);
	for(int i=tot; i--; ) ifac[i]=ifac[i+1]*(i+1llu)%P;
	f[0]=1;
	for(int i=m; i--; )
		for(int j=tot; j--; )
			for(int t=j; t; t&=t-1) {
				int k=t&-t;
				f[j]=(f[j]+arr(tot-a[i]-j+k, k-1)*(P-f[j-k])%P*k)%P;
			}
	for(int i=0; i<tot; ++i) ans=(ans+(u64)fac[tot-i-1]*f[i])%P;
	std::cout<<(u64)ans*tot%P<<std::endl;
	return 0;
}

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