inversionsum

inversionsum

Problem Statement

You are given an integer sequence of length N: A₁,A₂,...,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_Xi and A_Yi
• 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 10⁹+7.

Here, the inversion number of a sequence P₁,P₂,...,P_M is the number of pairs of integers (i,j) such that 1≤ i < j≤ M and P_i > P_j.

Constraints

• 1 ≤ N ≤ 3000
• 0 ≤ Q ≤ 3000
• 0 ≤ A_i ≤ 10⁹(1≤ i≤ N)
• 1 ≤ X_i,Y_i ≤ N(1≤ i≤ Q)
• X_i≠ Y_i(1≤ i≤ Q)
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Q
A1
:
AN
X1 Y1
:
XQ YQ

Output

Print the sum of the inversion numbers of the final sequences, modulo 10⁹+7.

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