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>
#define P 1000000007
#define int long long

using namespace std;

int n, S[233], F[2][100010], C[233][233], X;

signed main() {
	scanf("%lld%lld", &n, &X);
	for(int i = 0; i <= n; i++)
		for(int j = 0; j <= n; j++)
			C[i][j] = !j ? 1 : (C[i - 1][j - 1] + C[i - 1][j]) % P;
	for(int i = 1; i <= n; i++) scanf("%lld", &S[i]);
	sort(S + 1, S + n + 1);
	reverse(S + 1, S + n + 1);
	int a = 0, b = 1;
	F[0][X] = 1;
	for(int i = 1; i <= n; i++, swap(a, b)) {
		memset(F[b], 0, sizeof F[b]);
		for(int j = 0; j <= X; j++) {
			int t = j % S[i];
			F[b][t] = (F[b][t] + F[a][j]) % P;
			F[b][j] = (F[b][j] + F[a][j] * (n - i)) % P;
		}
	}
	int ans = 0;
	for(int i = 1; i <= X; i++) ans = (ans + i * F[a][i]) % P;
	printf("%d\n", (ans % P + P) % P);
	return 0;
}