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 int long long

const int MAX= 1E5+5;
const int MAXN = 205;
const int MOD = 1E9+7;

int n, X;
vector<int> a(MAXN);
int f[MAXN][MAX];

int dp(int i, int cur){
	int& ret = f[i][cur];
	if(ret != -1) return ret;
	if(i==0) return ret = (cur < a[1]? cur : 0);
	ret = (dp(i-1, cur%a[i]) + (i-1)*dp(i-1, cur))%MOD;
	return ret;
}

signed main() {
	cin >> n >> X;
	for(int i=1; i<= n; ++i) cin >> a[i];
	sort(a.begin()+1, a.begin()+n+1);
	int p = 1, ret = 0;
	memset(f, -1, sizeof f);
	for(int i=n; i>= 1; --i){
		ret += p*dp(i-1, X%a[i]);
		ret %= MOD;
		p *= (i-1);
		p%= MOD;
	}
	cout << ret;
	return 0;
}