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:
//Zory-2020
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
// typedef __int128 ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define FR first
#define SE second
#define MP make_pair
#define PB push_back
#define vc vector
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define bin(x) (1ll<<(x))
#define fo(i,l,r) for(int i=(l),I=(r);i<=I;i++)
#define fd(i,r,l) for(int i=(r),I=(l);i>=I;i--)
#define Debug printf("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define debug(x) cerr<<#x<<'='<<x<<endl
#define mem(x,val) memset(x,val,sizeof x)
namespace mine
{
    ll qread()
    {
        ll ans=0,f=1;char c=getchar();
        while(c<'0' or c>'9') {if(c=='-')f=-1;c=getchar();}
        while('0'<=c and c<='9') ans=ans*10+c-'0',c=getchar();
        return ans*f;
    }
    void write(ll num){if(num<0) putchar('-'),num=-num;if(num>=10) write(num/10);putchar('0'+num%10);}
    void write1(ll num){write(num);putchar(' ');}
    void write2(ll num){write(num);putchar('\n');}
    template<typename T>inline bool chmax(T&a,const T&b){return a<b?a=b,1:0;}
    template<typename T>inline bool chmin(T&a,const T&b){return a>b?a=b,1:0;}
    ll gcd(ll x,ll y){return y?gcd(y,x%y):x;}
    bool IN(ll x,ll l,ll r){return l<=x and x<=r;}

    const int INF=0x3f3f3f3f;
    const int MOD=1e9+7;
    int mm(const int x){return x>=MOD?x-MOD:x;}
    template<typename T> void add(T &x,const int &y){x=(x+y>=MOD?x+y-MOD:x+y);}
    ll qpower(ll x,ll e,int mod=MOD){ll ans=1;while(e){if(e&1)ans=ans*x%mod;x=x*x%mod;e>>=1;}return ans;}
    ll invm(ll x){return qpower(x,MOD-2);}
    const int N=1e3+10;

    int C[N][N],f[100][N];
    void main()
	{
        C[0][0]=1;fo(i,1,N-1){C[i][0]=1;fo(j,1,i)C[i][j]=mm(C[i-1][j-1]+C[i-1][j]);}
        int n=qread(),k=qread();f[0][n]=1;
        fo(id,1,k)
        {
            int a=qread();
            fo(i,0,n) fo(t,0,i)
                add(f[id][i-t],1ll*f[id-1][i]* C[i][t]%MOD*C[n-t][n-a]%MOD );
        }
        write(f[k][0]);
	}
};//(ans+MOD)%MOD
signed main()
{
    srand(time(0));
    mine::main();
}