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 MOD (1000000000+ 7)
#define MAX 200

int N, X;
int S[MAX];

long long dp[MAX + 1][100000 + 1];

int main() {
	cin >> N >> X;
	for( int i = 0; i < N; i++ ) {
		cin >> S[i];
	}

	sort( S, S + N, greater<int>() );
	dp[0][X] = 1;
	for( int i = 0; i < N; i++ ) {
		for( int j = 0; j <= X; j++ ) {
			dp[i + 1][j] = dp[i][j] * (N - 1- i) % MOD;
			dp[i + 1][j % S[i]] += dp[i][j];
			dp[i + 1][j % S[i]] %= MOD;
		}
	}
	long long ans = 0;
	for( int j = 0; j <= X; j++ ) {
		ans += dp[N][j] * j % MOD;
		ans %= MOD;
	}

	cout << ans << endl;

	return 0;
}
