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<algorithm>
const long long mod = 1e9+7;
long long f[201][100001];
int s[201];

int main(){
	int n,x;
	scanf("%d%d",&n,&x);
	for(int i = 1; i <= n; i++) scanf("%d",&s[i]);
	std::sort(s+1,s+1+n);
	for(int i = 0; i <= x; i++) f[1][i] = i%s[1];
	for(int i = 2; i <= n; i++){
		f[i][0] = 0;
		for(int j = 1; j <= x; j++){
			f[i][j] = f[i-1][j%s[i]] + (long long)(i-1)*f[i-1][j]%mod;
			if(f[i][j]>=mod) f[i][j] -= mod;
			//printf("f[%d][%d] = %lld\n",i,j,f[i][j]);
		}
	}
	printf("%lld\n",f[n][x]);
	return 0;
}
