Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

2 19
3 7

Sample Output 1

3

There are two possible orders in which we remove the numbers from S.

If we remove 3 and 7 in this order, the number on the blackboard changes as follows: 19 \rightarrow 1 \rightarrow 1.

If we remove 7 and 3 in this order, the number on the blackboard changes as follows: 19 \rightarrow 5 \rightarrow 2.

The output should be the sum of these: 3.

Sample Input 2

5 82
22 11 6 5 13

Sample Output 2

288

Sample Input 3

10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009

Sample Output 3

279669259

Be sure to compute the sum modulo 10^{9}+7.

Solution in JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";
function I(s,f){this._s=s.split("\n");this._c=0;this._l=0;this._f=f||Number}I.prototype.a=function(){var l=this._s[this._l];if(!l)return;var t=l.trim().split(" ");var a=t[this._c];this._c++;if(t.length===this._c){this._c=0;this._l++}return this._f(a)};I.prototype.l=function(){var l=this._s[this._l];if(!l)return;this._c=0;this._l++;return l.split(" ").map(this._f)};
function buildArray(r,t){let l=t||0;for(let t=r.length;t>0;t--){const n=r[t-1];l=Array(n).fill().map(()=>JSON.parse(JSON.stringify(l)))}return l}

var mod = 1e9 + 7;
function abmod(){for(var a=arguments,r=a[0],i=1;i<a.length;)r=((r>>16)*a[i]%mod*65536+(r&65535)*a[i++])%mod;return r;}

function main(input) {
  var o = new I(input);

  var N = o.a();
  var X = o.a();
  
  var S = o.l();

  S.sort((a,b) => b - a);

  var dp1 = Array(X+1).fill(0);
  dp1[X] = 1;
  for (var i = 0; i< N; i++) {
    var dp2 = Array(X+1).fill(0);
    for (var j = 0; j<=X; j++) {
      dp2[j] += dp1[j] * (N-i-1);
      dp2[j] %= mod;

      var m = j%S[i];
      dp2[m] += dp1[j];
      dp2[m] %= mod;
    }
    dp1 = dp2;
  }

  var sum = 0;
  for(var i = 0; i < S[N-1]; i++){
    sum += abmod(i,dp1[i]);
  }

  console.log(sum % mod);
}


main(require("fs").readFileSync("/dev/stdin", "utf8"));