Maximize the Power

The power array has even length. In each operation, pick any two of its position values x and y, gain the sum of the closed interval arr[min(x,y)..max(x,y)], and then remove these two elements from power. Maximize the total gain after all operations, modulo 10^9+7.

输入格式

The input contains N and K, then N non-negative arr values, then K positions. This site adds 1≤N≤200000, 2≤K≤2000 with K even, every position in [0,N−1], and arr[i]≤10^9.

输出格式

Output the maximum total gain modulo 10^9+7.

样例 1

输入：

5 4
3 5 6 0 7
3 1 0 2

输出：

25

样例 2

输入：

3 2
1 2 3
0 2

输出：

6

样例 3

输入：

2 2
0 0
1 0

输出：

0