Alice is playing a new game recently. In this game, there are n different kinds of cards. We assume that Alice have ci pieces of cards for ith kind.

Alice is asked to divide them into mm piles and then arrange each pile in one line. After that, Alice will get mm sequences. For convenience, 

the sequences are labeled S1,S2,⋯,SmS1,S2,⋯,Sm. For each i<j, Alice will get some points, equal to the length of 

the LCS(longest common subsequence) of Si and Sj. The total points is the sum of points for all i<j.

Now Alice is wondering the maximum points she can get.

As is known to everyone of you, Bob loves Alice very much. Could you tell Bob the answer to help Bob leave a good impression on Alice.

Input

The first line contains 2 integers m and n, indicating the number of sequences and the number of different kinds of card.

The second line contains n integers ci, indicating the number of ith card.

It is guaranteed that 1≤n,m≤100000,0≤ci≤100000     .

Output

Print the answer module 1000000007 in one line.

Sample input and output

2 2
2 3

2

Source

#include <iostream>
#include <cstdio>
using namespace std;
const int HASH = 1000000007;
int main()
{
    int m, n, c;
    long long ans = 0;
    scanf("%d%d", &m, &n);
    for(int i = 1; i <= n; i++){
        scanf("%d", &c);
        ans = (ans + (c/m)*(m*(m-1)/2) + (c%m)*(c%m-1)/2) % HASH;
    }
    printf("%lld", ans);
    return 0;
}