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;
using ll = long long;
ll MOD = 1e9+7;
ll add(ll a, ll b)
{
    return (a+b)%MOD;
}
int main()
{
    ll n, x;
    cin >> n >> x;
    vector<ll> s(n);
    for(int i = 0; i < n; i++)
    {
        cin >> s[i];
    }
    sort(s.begin(), s.end());
    reverse(s.begin(), s.end());
    vector<vector<ll>> dp(201, vector<ll>(100010));

    dp[0][x] = 1;
    for(int i = 1; i <= n; i++)
    {
        for(int j = 0; j <= 100010; j++)
        {
            dp[i][j] = add(dp[i][j], dp[i-1][j] * (n-i));
            dp[i][j%s[i-1]] = add(dp[i][j%s[i-1]], dp[i-1][j]);
        }
    }
    ll ans = 0;
    for(int i = 0; i <= 100010; i++)
    {
        ans = add(ans, dp[n][i]*i);
    }
    cout << ans << endl;
}
