After receiving the intel from Julian (don't worry, he is completely safe), Geven now has to analyse it. Some statistics are already well known (such as squirrels being reptiles with a life span rivalling Greenland sharks). Unfortunately, due to the harrowing escape from the squirrels, some of Julian's intel is missing. Geven notices that the squirrel armada is actually formed in a line, with teleport portals along it. To procure the necessary statistics for the AAC committee, Geven must perform some complex maths involving the entity known as RNG (black magic).

There are $N$ checkpoints connected together by $N-1$ paths, where the $i$-th path connects checkpoint $i$ to checkpoint $i+1$ and requires $a_i$ minutes to pass through. To make travelling faster, $M$ checkpoints have portals that one can choose to take in order to arrive immediately at any other portal.

Define $f(i,j)$ as the minimum time needed to travel from checkpoint $i$ to $j$. Find the sum of $f(i,j)$ over all $(i,j)$ where $1\le i<j\le N$. Since this number may be extremely large, output it modulo ${10}^9+7$.

Constraints

$2\le M\le N\le {10}^6$

$1\le a_i\le {10}^3$

Subtask 1 [10%]

$2\le N\le 3\times {10}^3$

Subtask 2 [40%]

$M=2$

Subtask 3 [50%]

No additional constraints. This batch will only run if subtask $1$ and subtask $2$ are successfully completed.

Input Specification

The first line of input contains two integers $N$, and $M$.

The second line of input contains $M$ space separated integers, the checkpoints which have portals.

The third line of input contains $N-1$ space separated integers representing $a_i$ for all $i$ $(1\le i<N)$.

Output Specification

Output one integer, the minimum cost to travel from each checkpoint to every other checkpoint modulo ${10}^9+7$.

Sample Input 1

5 2
2 5
4 6 1 7

Sample Output 1

56

Explanation for Sample Output 1

Travelling from checkpoint $1$ will take $4$ minutes to reach checkpoint $2$, $10$ minutes to reach checkpoint $3$, $11$ minutes to reach checkpoint $4$, and $4$ minutes to reach checkpoint $5$.

Travelling from checkpoint $2$ will take $6$ minutes to reach checkpoint $3$, $7$ minutes to reach checkpoint $4$, and $0$ minutes to reach checkpoint $5$.

Travelling from checkpoint $3$ will take $1$ minute to reach checkpoint $4$, and $6$ minutes to reach checkpoint $5$.

Lastly, it will take $7$ minutes to reach checkpoint $5$ from checkpoint $4$.

Adding all of these values up yields $56$, the minimal amount of time required.

Sample Input 2

10 3
9 3 8
3 8 4 1 4 4 3 4 4

Sample Output 2

334