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 F first
#define S second
#define PB push_back
#define all(x) x.begin(), x.end()

typedef long long ll; 
typedef long double ld;

const int N = 1000 * 100 + 10, M = 210; 
const int mod = 1000 * 1000 * 1000 + 7;

int dp[M][N];
int a[M];

int32_t main()
{
	ios::sync_with_stdio(0); cin.tie(0);
	int n, k;
	cin>> n >> k;
	for(int i = 0; i < n; i++) cin>> a[i];
	sort(a, a + n);
	for(int i = 0; i <= k; i++) dp[0][i] = i % a[0];
	for(int i = 1; i < n; i++) for(int j = 0; j <= k; j++)
	{
		dp[i][j] = 1ll * dp[i - 1][j] * i % mod + dp[i -1][j % a[i]];
		dp[i][j] %= mod;
	}
	cout<< dp[n-1][k] << endl;
}
