Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.

He wrote an integer X on the blackboard, then performed the following operation N times:

* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.



There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.

Constraints

* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.

Input

Input is given from Standard Input in the following format:


N X
S_1 S_2 \ldots S_{N}


Output

Print the answer.

Examples

Input

2 19
3 7


Output

3


Input

5 82
22 11 6 5 13


Output

288


Input

10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009


Output

279669259
#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
const int N=205,M=1e5+5;
const int mod=1e9+7;
int dp[N][M],a[N],n,X;
int dfs(int u,int x) {
    if(!u) return x%a[u];
    if(dp[u][x]!=-1) return dp[u][x];
    return dp[u][x]=(dfs(u-1,x%a[u])+1LL*u*dfs(u-1,x))%mod;
}
int main() {
    scanf("%d%d",&n,&X);
    for(int i=0;i<n;i++) scanf("%d",a+i);
    std::sort(a,a+n);
    memset(dp,-1,sizeof(dp));
    printf("%d\n",dfs(n-1,X));
    return 0;
}
