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<cstdio>
const int N=3005,P=1e9+7;
const long long I=5e8+4;
int n,q,v[N],f[N][N],a;
int main()
{
	scanf("%d%d",&n,&q);
	for(int i=1;i<=n;++i)
		scanf("%d",&v[i]);
	for(int i=1;i<=n;++i)
		for(int j=i+1;j<=n;++j)
			if(v[i]>v[j])++f[i][j];
			else if(v[i]<v[j])++f[j][i];
	for(int i=1,x,y;i<=q;++i)
	{
		scanf("%d%d",&x,&y);
		for(int j=1;j<=n;++j)if(j!=x&&j!=y)
			f[x][j]=f[y][j]=I*(f[x][j]+f[y][j])%P,f[j][x]=f[j][y]=I*(f[j][x]+f[j][y])%P;
		f[x][y]=f[y][x]=I*(f[x][y]+f[y][x])%P;
	}
	for(int i=1;i<=n;++i)
		for(int j=i+1;j<=n;++j)
			(a+=f[i][j])%=P;
	for(int i=1;i<=q;++i)(a*=2)%=P;
	return printf("%d",a),0;
}