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 ll long long 
using namespace std;
const int _=3e3+20,yl=1e9+7;
ll f[_][_],a[_],g[_],h[_],n,q,p;
ll POW(ll x,ll y){
	ll res=1;
	while(y){
		if(y&1)res=res*x%yl;
		x=x*x%yl;y>>=1;
	}
	return res;
}
int main(){
	ios::sync_with_stdio(false);
	cin>>n>>q;p=POW(2,yl-2);
	for(int i=1;i<=n;++i){
		cin>>a[i];
		for(int j=0;j<i;++j){
			if(a[j]<a[i])f[i][j]=1;
			if(a[j]>a[i])f[j][i]=1;
		}
	}
	for(int i=1;i<=q;++i){
		int x,y;cin>>x>>y;
		for(int i=1;i<=n;++i){
			g[i]=(f[x][i]+f[y][i])*p%yl;
			h[i]=(f[i][x]+f[i][y])*p%yl;
		}
		for(int i=1;i<=n;++i){
			if(i==x||i==y)continue;
			f[x][i]=f[y][i]=g[i];
			f[i][x]=f[i][y]=h[i];
		}
		f[x][y]=f[y][x]=(f[x][y]+f[y][x])*p%yl;
	}
	ll ans=0;
	for(int i=1;i<=n;++i)
		for(int j=i+1;j<=n;++j)
			ans+=f[i][j];
	ans=ans%yl*POW(2,q)%yl;
	cout<<ans<<endl;
}