Goat II

Goat II

Problem Statement

Andy the goat is very hungry. Luckily, there is a line of $n$ tufts of grass directly in front of him in a line. However, the $i$-th tuft of grass takes $A_i$ seconds to eat.

Andy has $q$ questions, each of the form "How many tufts of grass could I eat in $B_i$ seconds?". Note that he must eat the tufts in the order given in the input.

Input

The first line of input will consist of two integers, $n$ and $q$.

The second line of input will consist of $n$ integers, the array $A$.

The third line of input will consist of $q$ integers, each being the amount of tufts Andy is thinking about in one question.

Output

The output should consist of a single line of $q$ integers, one for each question.

Constraints

For all test cases:

• $1 \le n \le 10^5$
• $1 \le q \le 10^5$
• $1 \le A[i] \le 10^3$
• $1 \le B[i] \le 10^8$

Sample Test Cases

Example 1

3 2
1 5 9
7 16

2 3

Explanation

In $7$ seconds, Andy can eat the first two tufts of grass (takes $1 + 5 = 6$ seconds).

In $16$ seconds, Andy can eat all three tufts of grass (takes $1 + 5 + 9 = 15$ seconds).