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 Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define Reg register
#define RI Reg int
#define Con const
#define CI Con int&
#define I inline
#define W while
#define N 3000
#define X 1000000007
#define I2 500000004
using namespace std;
int n,m,a[N+5],f[N+5][N+5];
int main()
{
	RI i,j,x,y;for(scanf("%d%d",&n,&m),i=1;i<=n;++i) scanf("%d",a+i);
	for(i=1;i<=n;++i) for(j=1;j<=n;++j) a[i]<a[j]&&(f[i][j]=1);
	for(i=1;i<=m;++i)
	{
		scanf("%d%d",&x,&y),f[x][y]=f[y][x]=1LL*I2*(f[x][y]+f[y][x])%X;
		for(j=1;j<=n;++j) j^x&&j^y&&(f[x][j]=f[y][j]=1LL*I2*(f[x][j]+f[y][j])%X);
		for(j=1;j<=n;++j) j^x&&j^y&&(f[j][x]=f[j][y]=1LL*I2*(f[j][x]+f[j][y])%X);
	}
	RI ans=0;for(i=1;i<=n;++i) for(j=1;j^i;++j) ans=(ans+f[i][j])%X;
	for(i=1;i<=m;++i) ans=2LL*ans%X;return printf("%d\n",ans),0;
}