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 <iostream>
#include <algorithm>
#define llint long long
#define mod 1000000007

using namespace std;

int n, x;
int s[205];
llint dp[205][100005];

int main(void)
{
	cin >> n >> x;
	for(int i = 1; i <= n; i++) cin >> s[i];
	sort(s+1, s+n+1);
	reverse(s+1, s+n+1);
	
	dp[0][x] = 1;
	for(int i = 0; i < n; i++){
		for(int j = 0; j <= x; j++){
			(dp[i+1][j%s[i+1]] += dp[i][j]) %= mod;
			(dp[i+1][j] += dp[i][j] * (n-i-1) % mod) %= mod;
		}
	}
	
	llint ans = 0;
	for(int i = 0; i < s[n]; i++){
		ans += dp[n][i] * i % mod, ans %= mod;
	}
	cout << ans << endl;
	
	return 0;
}