You have been given an array of ~N~ unique integers (with starting index ~1~) and ~Q~ queries to perform. For each query, you are given an index ~j~. For each integer in the array, you must calculate the product of the integer and the distance between their index and the given index ~j~. That is, if the integer has index ~i~ you must calculate ~x_i\times(|i-j|)~. Output, for each query, the sum of the calculations for all integers in the array, modulo ~10^9+7~.

Input Specification

The first line will contain two integers, ~N~ and ~Q~ ~(1 \leq N, Q \leq 10^5)~, separated by a space. The second line will contain ~N~ space-separated unique integers, ~x_1, x_2, \ldots, x_N~ ~(0 \leq x_i \leq 10^4)~. The next ~Q~ lines will contain one integer, an index ~y~ ~(1 \leq y \leq N)~.

Output Specification

Output, on separate lines, the answer to each query, modulo ~10^9+7~.

Subtasks

Subtask 1 [20%]

~N \leq 10^3~

~Q \leq 10^3~

Subtask 2 [80%]

No additional constraints.

Sample Input 1

9 5
10 6 4 5 6 4 11 9 3 
8
3
7
5
2

Sample Output 1

186
162
152
136
188

Sample Input 2

9 3
4 5 4 11 11 10 7 9 6 
4
2
8

Sample Output 2

144
234
188

Explanation for Sample Input 1

For the first query, ~j = 8~. The calculations then become: ~10\times7+6\times6+4\times5+5\times4+6\times3+4\times2+11\times1+9\times0+3\times1 = 186~