Yesterday Chef had a great party and doesn't remember the way he celebreated it. But he found a strange paper in his kitchen containing n digits (lets give them indices from 1 to n and name them a1, a2 ... aN).
Chef remembers that he played such game:

On each step he choose an index x from 1 to n.
For all indices y (y < x) he calculated the difference by = ax - ay.
Then he calculated B1 - sum of all by which are greater than 0 and B2 - sum of all by which are less than 0.
The answer for this step is B1 - B2.

Chef remembers the game, but forgot the answer. Please, help him!

Input

The first line contains two integers n, m denoting the number of digits and number of steps. The second line contains n digits (without spaces) a1, a2, ..., an.
Each of next m lines contains single integer x denoting the index for current step.

Output

For each of m steps print single number in a line - answer of the step.

Constraints

1 ≤ n, m ≤ 10^5
0 ≤ ai ≤ 9
1 ≤ x ≤ n

Example
Input:
10 3
0324152397
1
4
7

Output:
0
7
9

Explanation
For index 1 there are no indexes which are less, so B1 = B2 = 0 and the answer is 0.
For index 4 we have

b1 = 4-0=4,
b2 = 4-3=1,
b3 = 4-2=2,

so B1 = 4+1+2 = 7, B2 = 0
and the answer is 7.
For index 7 we have

b1 = 2-0=2,
b2 = 2-3=-1,
b3 = 2-2=0,
b4 = 2-4=-2,
b5 = 2-1=1,
b6 = 2-5=-3,

so B1 = 2 + 1 = 3,
B2 = -1 -2 -3 = -6
and the answer is 9.

见题面

见题面