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>
#include <functional>

long long num[100001][2] = { 0 };

long long MOD = 1000000007LL;
int main()
{
	int S[202];
	int N, X;
	scanf("%d%d", &N, &X);
	for (int i = 0; i < N; i++) {
		scanf("%d", &S[i]);
	}
	std::sort(S, S + N, std::greater<int>());

	num[X][0] = 1;
	int cur = 0, next = 1;
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < 100001; j++) {
			num[j % S[i]][next] += num[j][cur];
			num[j % S[i]][next] %= MOD;

			num[j][next] += num[j][cur] * (N - i - 1);
			num[j][next] %= MOD;
		}
		for (int j = 0; j < 100001; j++) {
			num[j][cur] = 0;
		}
		std::swap(cur, next);
	}

	long long ans = 0;
	for (int i=0; i<100001; i++) {
		ans += i * num[i][cur];
		ans %= MOD;
	}

	printf("%lld\n", ans);
}
