### Problem Statement

You are given an integer sequence of length N: A1,A2,...,AN. Let us perform Q operations in order. The i-th operation is described by two integers Xi and Yi. In this operation, we will choose one of the following two actions and perform it:

• Swap the values of AXi and AYi
• Do nothing

There are 2Q 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,...,PM is the number of pairs of integers (i,j) such that 1≤ i < j≤ M and Pi > Pj.

### Constraints

• 1 ≤ N ≤ 3000
• 0 ≤ Q ≤ 3000
• 0 ≤ Ai ≤ 109(1≤ i≤ N)
• 1 ≤ Xi,Yi ≤ N(1≤ i≤ Q)
• Xi≠ Yi(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.

```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.

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

```36
```

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

```425
```

### Submitting .cpp to 'inversionsum'

Time Limit: 3 Seconds
Memory Limit: 1024MB
No. of ACs: 2