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: Wrong Answer)

function Main(input){
  var ary = [];
  for(var i=0;i<input.split("\n")[0].split(" ")[0];i++){
  	ary.push(1);
  }
  var str = input.split("\n")[1];
  var newAry = [];
  for(var j=0;j<ary.length;j++){
      newAry.push();
  }
  for(var i=2;i<input.split("\n").length;i++){
  	var jumon = input.split("\n")[i].split(" ");
    for(var j in newAry)newAry[j]=0;
    if(jumon[1]=="L"){
      for(var j=0;j<str.length;j++){
        if(j!=0||str[j]!=jumon[0])newAry[str[j]==jumon[0]?j-1:j]+=ary[j];
      }
    }else{
      for(var j=0;j<str.length;j++){
        if(j!=ary.length-1||str[j]!=jumon[0])newAry[str[j]==jumon[0]?j+1:j]+=ary[j];
      }
    }
    ary=newAry.concat();
  }
  var golems = 0;
  for(var i of ary)golems+=i;
  console.log(golems);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));