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 fo(i,a,b)for(int i=a,_e=b;i<=_e;++i)
#define ll long long
using namespace std;
const int N=3005,mo=1e9+7,mo2=mo+1>>1;
int n,q,x,y,p[N];
int f[N][N],ans,xs;
int r[N],c[N];
int main(){
	cin>>n>>q;
	fo(i,1,n)cin>>p[i];
	fo(i,1,n)fo(j,1,n)
		if(p[i]<p[j])f[i][j]=1;
	for(xs=1;q--;xs=(ll)xs*2%mo){
		cin>>x>>y;
		fo(i,1,n){
			r[i]=(ll)(f[x][i]+f[y][i])*mo2%mo;
			c[i]=(ll)(f[i][x]+f[i][y])*mo2%mo;
		}
		fo(i,1,n)f[x][i]=f[y][i]=r[i],f[i][x]=f[i][y]=c[i];
		f[x][x]=f[y][y]=0;
		f[x][y]=f[y][x]=(f[x][y]+f[y][x])%mo;
	}
	fo(i,1,n)fo(j,1,i-1)ans=(ans+f[i][j])%mo;
	cout<<(ll)ans*xs%mo;
}