Inversion Sum

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

inputFormat

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

outputFormat

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

样例

3 2
1
2
3
1 2
1 3

6