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: Time Limit Exceeded)

"use strict";

// read lines from stdin
const input = require("fs")
  .readFileSync("/dev/stdin", "utf8")
  .split("\n");

const firstLine = input[0].split(" ").map((val) => parseInt(val, 10));
const N = firstLine[0];
const X = firstLine[1];

const S = input[1].split(" ").map((val) => parseInt(val, 10));

function sumMod(X, ary) {
  let sum = 0;

  if (ary.length === 1) {
    return X % ary[0];
  }

  for (let i = 0; i < ary.length; i++) {
    const num = ary[i];
    const nextX = X % num;

    sum += sumMod(nextX, ary.slice(0, i).concat(ary.slice(i + 1, ary.length)));
  }

  return sum %= 1000000000 + 7;
}

console.log(sumMod(X, S));