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 <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int MOD = 1e9 + 7;
const int N = 202;

int n,x,s[N];
int fac[N];
LL dp[202][100000 + 10];
LL A[202][202];
int main() {
	scanf("%d%d",&n,&x);
	for(int i=1;i<=n;i++){
		scanf("%d", &s[i]);
	}
	dp[0][x] = 1;
	sort(s + 1, s + 1 + n);
	for (int i = 0; i <= n; i ++) {
		for (int j = 0; j <= x; j ++) {
			if (dp[i][j] == 0) continue;
			int cnt = n - i;
			for (int k = 1; k <= n; k ++) {
				if (s[k] <= j) {
					(dp[i+1][j % s[k]] += dp[i][j]);
					if (dp[i+1][j % s[k]] > MOD) dp[i+1][j%s[k]] -= MOD;
					cnt --;
				} else {
					break;
				}
			}
			(dp[i+1][j] += dp[i][j] * cnt) %= MOD;
		}
	}
	LL ans = 0;
	for (int i = 0; i <= x; i ++) {
		ans = (ans + dp[n][i] * i) % MOD;
	}
	cout << ans << endl;

}	