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>

const int N = 3010, P = 1e9 + 7, I2 = (P + 1) / 2;

int n, q, A[N], f[N][N], pw[N], ans;

int main() {
  scanf("%d %d", &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)
      if (i != j)
        f[i][j] = A[i] < A[j];
  for (int i = 1; i <= q; ++i) {
    int x, y; scanf("%d %d", &x, &y);
    f[x][y] = f[y][x] = 1ll * (f[x][y] + f[y][x]) * I2 % P;
    for (int j = 1; j <= n; ++j)
      if (j != x && j != y) {
        f[j][x] = f[j][y] = 1ll * (f[j][x] + f[j][y]) * I2 % P;
        f[x][j] = f[y][j] = 1ll * (f[x][j] + f[y][j]) * I2 % P;
      }
  }
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j < i; ++j)
      ans = (ans + f[i][j]) % P;
  for (int i = 1; i <= q; ++i)
    ans = ans * 2 % P;
  std::cout << ans << std::endl;
  return 0;
}