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<stdio.h>
typedef long long ll;
const int mod=1e9+7,i2=(mod+1)/2;
int mul(int a,int b){return(ll)a*b%mod;}
void inc(int&a,int b){(a+=b)>=mod?a-=mod:0;}
int a[3010],f[3010][3010];
int main(){
	int n,q,i,j,x,y,s;
	scanf("%d%d",&n,&q);
	for(i=1;i<=n;i++)scanf("%d",a+i);
	for(i=1;i<=n;i++){
		for(j=1;j<=n;j++)f[i][j]=a[i]>a[j];
	}
	for(j=1;j<=q;j++){
		scanf("%d%d",&x,&y);
		f[x][y]=f[y][x]=mul(f[x][y]+f[y][x],i2);
		for(i=1;i<=n;i++){
			if(i!=x&&i!=y){
				f[x][i]=f[y][i]=mul(f[x][i]+f[y][i],i2);
				f[i][x]=f[i][y]=mul(f[i][x]+f[i][y],i2);
			}
		}
	}
	s=0;
	for(i=1;i<n;i++){
		for(j=i+1;j<=n;j++)inc(s,f[i][j]);
	}
	while(q--)s=mul(s,2);
	printf("%d",s);
}