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>
#include <vector>
#include <string>
#include <cmath>

using namespace std;

const long long mod = 1e9 + 7;

long long dp[201][100001];
long long N, X;
long long S[201];

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