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>
#include<cstdlib>
#include<cstring>
#include<iostream>
#define LL long long
using namespace std;
const LL mod=1e9+7;
LL n,q,a[3010],Q;
LL f[3010][3010];
LL fp(LL a,LL b)
{
	LL ans=1;
	while(b)
	{
		if(b&1) ans=ans*a%mod;
		a=a*a%mod;b>>=1;
	}
	return ans;
}
const LL inv=fp(2,mod-2);
int main()
{
	scanf("%lld %lld",&n,&q);Q=q;
	for(LL i=1;i<=n;i++) scanf("%lld",&a[i]);
	for(LL i=1;i<=n;i++)
		for(LL j=1;j<=n;j++) f[i][j]=(a[i]<a[j]);
	while(q--)
	{
		LL x,y;scanf("%lld %lld",&x,&y);
		f[x][y]=f[y][x]=(f[x][y]+f[y][x])*inv%mod;
		for(LL i=1;i<=n;i++)
			if(i!=x&&i!=y)
			{
				f[i][x]=f[i][y]=(f[i][x]+f[i][y])*inv%mod;
				f[x][i]=f[y][i]=(f[x][i]+f[y][i])*inv%mod;
			}
	}
	LL ans=0;
	for(LL i=1;i<=n;i++)
		for(LL j=1;j<i;j++) (ans+=f[i][j])%=mod;
	(ans*=fp(2,Q))%=mod;
	printf("%lld",ans);
}