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