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

Input

3 2
1 5 9
7 16

Output

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).