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 <stdio.h>
#include <algorithm>
using namespace std;
const int mod = 1000000007;
int mul(long long a, long long b){
	return a * b % mod;
}
const int maxn = 202;
const int maxx = 100001;
int a[maxn], f[maxn][maxx];
int main(){
	int n, x; scanf("%d %d", &n, &x);
	for(int i = 0; i < maxx; i++) f[0][i] = i;
	for(int i = 1; i <= n; i++) scanf("%d", a + i);
	sort(a + 1, a + 1 + n);
	for(int i = 1; i <= n; i++){
		int v = a[i];
		for(int j = 0; j < maxx; j++){
			f[i][j] = mul(f[i-1][j], i - 1) + f[i - 1][j % v];
			if (f[i][j] >= mod) f[i][j] -= mod;
		}
	}
	printf("%d\n", f[n][x]);
	return 0;
}

