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;

typedef long long i64;

const i64 NMAX = 200;
const i64 VMAX = 1e5;
const i64 MOD  = 1e9 + 7;

i64 d[NMAX+2][VMAX+2];
i64 v[NMAX+2];
i64 N, start;

int main()
{
    cin >> N >> start;
    for( i64 i = 1;  i <= N;  ++i ) {
        cin >> v[i];
    }
    sort( v +1, v+N+1 );
    for( i64 val = 0;  val <= VMAX;  ++val )
        d[1][val] = val % v[1];
    for( i64 i = 2;  i <= N;  ++i ) {
        for( i64 val = 0;  val <= VMAX;  ++val ) {
            d[i][val] = d[i - 1][val % v[i]] + 1LL * (i - 1) * (d[i - 1][val]);
            d[i][val] %= MOD;
        }
    }
    cout << d[N][start] << '\n';
    return 0;
}
