Problem: You are given an integer sequence of length N: A_1,A_2,...,A_N. Let us perform Q operations in order. The i-th operation is described by two integers X_i and Y_i. In this operation, we will choose one of the following two actions and perform it:

* Swap the values of A_{X_i} and A_{Y_i}
* Do nothing



There are 2^Q ways to perform these operations. Find the sum of the inversion numbers of the final sequences for all of these ways to perform operations, modulo 10^9+7.

Here, the inversion number of a sequence P_1,P_2,...,P_M is the number of pairs of integers (i,j) such that 1\leq i < j\leq M and P_i > P_j.

Constraints

* 1 \leq N \leq 3000
* 0 \leq Q \leq 3000
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* 1 \leq X_i,Y_i \leq N(1\leq i\leq Q)
* X_i\neq Y_i(1\leq i\leq Q)
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N Q
A_1
:
A_N
X_1 Y_1
:
X_Q Y_Q


Output

Print the sum of the inversion numbers of the final sequences, modulo 10^9+7.

Examples

Input

3 2
1
2
3
1 2
1 3


Output

6


Input

5 3
3
2
3
1
4
1 5
2 3
4 2


Output

36


Input

9 5
3
1
4
1
5
9
2
6
5
3 5
8 9
7 9
3 2
3 8


Output

425

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define mod 1000000007
using namespace std;
int n, q, num[3007], p[3007][3007], res;
int main()
{
	cin >> n >> q;
	for (int i = 1; i <= n; i++)
		cin >> num[i];
	for (int i = 1; i <= n; i++)
		for (int j = 1; j <= n; j++)
			p[i][j] = num[i] > num[j];
	for (int i = 1, a, b; i <= q; i++)
	{
		cin >> a >> b;
		p[a][b] = p[b][a] = 500000004LL * (p[a][b] + p[b][a]) % mod;
		for (int j = 1; j <= n; j++)
			if (j != a && j != b)
			{
				p[j][a] = p[j][b] = 500000004LL * (p[j][a] + p[j][b]) % mod;
				p[a][j] = p[b][j] = 500000004LL * (p[a][j] + p[b][j]) % mod;
			}
	}
	for (int i = 1; i <= n; i++)
		for (int j = i + 1; j <= n; j++)
			res = (res + p[i][j]) % mod;
	for (int i = 1; i <= q; i++)
		res = (res << 1) % mod;
	cout << res << endl;
	return 0;
}