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 long long mod=1e9+7,inv2=(mod+1)/2;
int n,q,a[4001],dp[4001][4001];
int main() {
	cin>>n>>q; for(int i=1;i<=n;i++)cin>>a[i]; for(int i=1;i<=n;i++) for(int j=1;j<=n;j++)dp[i][j]=(a[i]>a[j]);
	for(int k=1,x,y;k<=q;k++) {
		cin>>x>>y; dp[x][y]=dp[y][x]=1ll*inv2*(dp[x][y]+dp[y][x])%mod;
		for(int i=1;i<=n;i++) if(i!=x&&i!=y)dp[i][x]=dp[i][y]=1ll*inv2*(dp[i][x]+dp[i][y])%mod,dp[x][i]=dp[y][i]=1ll*inv2*(dp[x][i]+dp[y][i])%mod;
	}
	long long ans=0; for(int i=1;i<=n;i++) for(int j=i+1;j<=n;j++)ans+=dp[i][j]; while(q--)ans=ans*2%mod;
	cout<<ans<<'\n';
}