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;
#define int long long
const int maxn=3200;
const int mod=1000000007,inv2=500000004;
int n,q,x,y,a[maxn],f[maxn][maxn],ans;
signed main()
{ cin>>n>>q;
  for (int i=1;i<=n;i++) cin>>a[i];
  for (int i=1;i<=n;i++)
  for (int j=1;j<=n;j++)
  f[i][j]=a[i]>a[j];
  for (int i=1;i<=q;i++)
  {  cin>>x>>y;
     for (int j=1;j<=n;j++)
     {  if (j==x || j==y)  continue;
	    f[j][y]=f[j][x]=(f[j][x]+f[j][y])*inv2%mod;
		f[x][j]=f[y][j]=(f[x][j]+f[y][j])*inv2%mod;  
	 }
	 f[x][y]=f[y][x]=(f[x][y]+f[y][x])*inv2%mod;
  }
  for (int i=1;i<=n;i++)
  for (int j=i+1;j<=n;j++)
  ans=ans+f[i][j];
  while (q--)  ans=ans*2%mod;
  cout<<ans<<endl;
}