Problem: There are N children, numbered 1,2,\ldots,N. In the next K days, we will give them some cookies. In the i-th day, we will choose a_i children among the N with equal probability, and give one cookie to each child chosen. (We make these K choices independently.)

Let us define the happiness of the children as c_1 \times c_2 \times \ldots \times c_N, where c_i is the number of cookies received by Child i in the K days. Find the expected happiness multiplied by \binom{N}{a_1} \times \binom{N}{a_2} \times \ldots \times \binom{N}{a_K} (we can show that this value is an integer), modulo (10^{9}+7).

Constraints

* 1 \leq N \leq 1000
* 1 \leq K \leq 20
* 1 \leq a_i \leq N

Input

Input is given from Standard Input in the following format:


N K
a_1 a_2 \ldots a_K


Output

Print the answer.

Examples

Input

3 2
3 2


Output

12


Input

856 16
399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63


Output

337587117

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define MAXN 1005
#define mod int(1e9+7)
using namespace std;
int N,M;
int a[MAXN];
long long f[25][MAXN];
long long jie[MAXN],ijie[MAXN];
long long kuaisumi(long long x,int y)
{
	long long ans=1;
	while(y)
	{
		if(y&1) ans=ans*x%mod;
		x=x*x%mod;
		y>>=1;
	}
	return ans;
}
void yuchuli()
{
	jie[0]=1; ijie[0]=1;
	for(int i=1;i<=N;i++)
	{
		jie[i]=(jie[i-1]*i)%mod;
		ijie[i]=kuaisumi(jie[i],mod-2);
	}
}
long long C(int x,int y)
{
	return jie[x]*ijie[y]%mod*ijie[x-y]%mod;
}
int main()
{
	cin>>N>>M;
	yuchuli();
	for(int i=1;i<=M;i++) cin>>a[i];
	f[0][0]=1;
	for(int i=1;i<=M;i++)
		for(int j=0;j<=N;j++)
			for(int k=0;k<=min(j,a[i]);k++)
				f[i][j]=(f[i-1][j-k]*C(N-j+k,k)%mod*C(N-k,a[i]-k)%mod+f[i][j])%mod;
	cout<<f[M][N]%mod;
	return 0;
}