Interval tree can be regarded as an extension of traditional segment tree: each vertex in interval tree still represents a interval, but the split points do not need to be the middle point.

For example, the following picture describe an interval tree on [1,6]:



Similar with segment tree, we can do some interval queries on interval tree. And we can define the time complexity of interval [l,r] as the number of vertices we need to visit when the query is about [l,r]. 

Formally, let S[l,r] be the set of vertices v on the interval tree which satisfy one of the following 2 conditions:
(1) v's interval is a subinterval of [l,r], but vv's father's interval is not. 
(2) At least one of v's decendants satisfies (1).


Now, given an interval tree on [1,n] and have q queries. Each query is a positive integer k, you need to find out the number of different intervals of which the time complexity is exactly k.

The input will consist of multiple test cases. Each case begins with two positive integer n and q. 

The second line contains n-1 integers, the split point of each non-leaf vertex, in the pre-order traversal. If vertex [l,r]'s split point is m, it's left child should be [l,m] and it's right child should be [m+1,r]. 

Then q lines follow. The i-th line of the following n lines is the integer k denoting the i-th query.

The input guarantees that l ≤ m < r, 1 ≤ n,q ≤ 105 , and 1 ≤ k ≤ 109  and the sum of n's and q's in all test cases will not exceed 500000.

For each query, output a single line with a single number, the answer.

6 7
5 1 3 2 4
1
2
3
4
5
6
7

1
2
2
3
6
4
3