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>
using namespace std;

const int MOD = 1e9 + 7; const long long INV2 = (MOD + 1) / 2;
int dp[3003][3003] , arr[3003] , N , Q , tms = 1;

int main(){
	cin >> N >> Q;
	for(int i = 1 ; i <= N ; ++i){
		cin >> arr[i];
		for(int j = i - 1 ; j ; --j){
			dp[i][j] = arr[j] < arr[i];
			dp[j][i] = arr[i] < arr[j];
		}
    }
	for(int i = 1 ; i <= Q ; ++i){
		int x , y; cin >> x >> y;
		for(int j = 1 ; j <= N ; ++j)
			if(j != x && j != y){
				dp[j][y] = dp[j][x] = (dp[j][x] + dp[j][y]) * INV2 % MOD;
				dp[x][j] = dp[y][j] = (dp[x][j] + dp[y][j]) * INV2 % MOD;
			}
		dp[x][y] = dp[y][x] = (dp[x][y] + dp[y][x]) * INV2 % MOD;
	}
	int sum = 0;
	for(int i = 1 ; i <= N ; ++i) for(int j = i + 1 ; j <= N ; ++j) sum = (sum + dp[i][j]) % MOD;
	for(int i = 1 ; i <= Q ; ++i) sum = (sum << 1) % MOD;
	cout << sum; return 0;
}