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;
#define rep(i,n) for(int i=0;i<n;i++)
#define int long long
const int mod = 1000000007;

int modpow(int a, int x) {
	int res = 1;
	while (x) {
		if (x & 1)res = res * a%mod;
		a = a * a%mod;
		x >>= 1;
	}
	return res;
}
int s[205];
int dp[205][100005];
signed main() {
	int n, x; cin >> n >> x;
	rep(i, n)cin >> s[i];
	sort(s, s + n);
	reverse(s, s + n);
	dp[0][x] = 1;
	rep(i, n) {
		int p = modpow(n - i, mod - 2);
		rep(j, x + 1) {
			if (!dp[i][j])continue;
			dp[i + 1][j%s[i]] += dp[i][j] * p%mod;
			dp[i + 1][j] += dp[i][j] * (mod + 1 - p) % mod;
			dp[i + 1][j] %= mod;
			dp[i + 1][j%s[i]] %= mod;
		}
	}
	int sum = 0;
	rep(i, x + 1)sum = (sum + i * dp[n][i]) % mod;
	rep(i, n) {
		sum *= (i + 1); sum %= mod;
	}
	cout << sum << endl;
}