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 Rust (1.15.1) (judge verdict: Wrong Answer)

// Try Exawizards 2019
// author: Leonardone @ NEETSDKASU

fn main() {
	let mut stdin = String::new();
    std::io::Read::read_to_string(
    	&mut std::io::stdin(),
        &mut stdin).unwrap();
	let mut stdin = stdin.split_whitespace();
    let mut get = || stdin.next().unwrap();
    macro_rules! get {
    	($t:ty) => (get().parse::<$t>().unwrap());
        () => (get!(i64));
    }
    
    // Wrong Answer
    
    let n = get!(usize);
    let x = get!(usize);
    let mut s = vec![];
    for _ in 0..n {
    	s.push(get!(usize));
    }
    let m = 1_000_000_007;
    let mut dp = vec![0_i64; 100000 + 1];
    let mut cnt = vec![vec![0; s.len()]; dp.len()];
    dp[x] = 1;
    for _ in 0..n {
    	let mut tmp = vec![0_i64; dp.len()];
        let mut tcn = vec![vec![0; s.len()]; dp.len()];
	    for k in 0..s.len() {
        	let p = s[k];
    		for i in 0..dp.len() {
        		let j = i % p;
            	tmp[j] = (tmp[j]+(dp[i]+m-cnt[i][k])) % m;
                for u in 0..n {
                	tcn[j][u] = (tcn[j][u] + cnt[i][u]) % m;
                }
                tcn[j][k] = (tcn[j][k] + 1) % m;
        	}
		}
        dp = tmp;
        cnt = tcn;
    }
    let mut ans = 0_i64;
    for i in 0..dp.len() {
    	let v = dp[i] * i as i64 % m;
        ans = (ans + v) % m;
    }
    println!("{}", ans);
}