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 <vector>
#include <algorithm>
using namespace std;

const int MOD = 1e+9 + 7;


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


    sort( S.begin(), S.end() );
    // dp[i]: 黒板に書かれた文字が i のとき, N回の操作をN!通り行った場合の数の総和
    vector<long long> dp(1000001);
    for( int i = 0; i <= X; ++i ) dp[i] = i;
    for( int i = 0; i < N; ++i ){
        for( int j = X; j > 0; --j ){
            dp[j] = ( i*dp[j] + dp[j%S[i]] ) % MOD;
        }
    }
    cout << dp[X] << endl;

    return 0;
}