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 rep(i,x,y) for (int i=(x);i<=(y);i++)
#define ll long long
using namespace std;
const int N=3005,mod=1e9+7,inv2=5e8+4;
int n,Q,a[N],f[N][N],ans,p;
int main(){
	scanf("%d%d",&n,&Q);
	rep (i,1,n) scanf("%d",&a[i]);
	rep (i,1,n) rep (j,1,n) f[i][j]=a[i]>a[j];
	p=1;
	while (Q--){
		int x,y; scanf("%d%d",&x,&y); p=(p+p)%mod;
		if (x>y) swap(x,y); if (x==y) continue;
		rep (i,1,n) if (x!=i&&y!=i){
			int v=(f[x][i]+f[y][i])%mod;
			f[x][i]=f[y][i]=(ll)v*inv2%mod;
			v=(f[i][x]+f[i][y])%mod;
			f[i][x]=f[i][y]=(ll)v*inv2%mod;
		}
		int v=(f[x][y]+f[y][x])%mod;
		f[x][y]=f[y][x]=(ll)v*inv2%mod;
	}
	rep (i,1,n) rep (j,i+1,n) (ans+=f[i][j])%=mod;
	printf("%lld\n",(ll)ans*p%mod);
	return 0;
}