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.

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 $10^9+7$.