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;
typedef long long ll;
const ll P=1e9+7,V=(P+1)>>1;
const int N=3005;
int n,q,a[N]; ll f[N][N],g[N][N],ans,s=1;
int main()
{
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	cin>>n>>q;
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	for(int i=1;i<=n;i++) for(int j=1;j<=n;j++){
		f[i][j]=(a[i]<a[j]); g[i][j]=(a[i]>a[j]);
	}
	while(q--){
		int x,y; scanf("%d%d",&x,&y);
		f[x][y]=f[y][x]=(f[x][y]+f[y][x])*V%P;
		g[x][y]=g[y][x]=(g[x][y]+g[y][x])*V%P;
		for(int i=1;i<=n;i++) if(i!=x && i!=y){
			f[x][i]=f[y][i]=(f[x][i]+f[y][i])*V%P;
			g[x][i]=g[y][i]=(g[x][i]+g[y][i])*V%P;
			f[i][x]=f[i][y]=(f[i][x]+f[i][y])*V%P;
			g[i][x]=g[i][y]=(g[i][x]+g[i][y])*V%P;
		}
		(s*=2)%=P;
	}
	for(int i=1;i<=n;i++) for(int j=i+1;j<=n;j++) (ans+=g[i][j])%=P;
	cout<<ans*s%P<<endl;
	return 0;
}