Problem Statement

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.

Sample Input 1

3 2
1
2
3
1 2
1 3

Sample Output 1

6

There are four ways to perform operations, as follows:

• Do nothing, both in the first and second operations. The final sequence would be 1,2,3, with the inversion number of 0.
• Do nothing in the first operation, then perform the swap in the second. The final sequence would be 3,2,1, with the inversion number of 3.
• Perform the swap in the first operation, then do nothing in the second. The final sequence would be 2,1,3, with the inversion number of 1.
• Perform the swap, both in the first and second operations. The final sequence would be 3,1,2, with the inversion number of 2.

The sum of these inversion numbers, 0+3+1+2=6, should be printed.

Sample Input 2

5 3
3
2
3
1
4
1 5
2 3
4 2

Sample Output 2

36

Sample Input 3

9 5
3
1
4
1
5
9
2
6
5
3 5
8 9
7 9
3 2
3 8

Sample Output 3

425