You have a weakness for adopting cats from the local pet shelter. Every time you walk by, you impulsively adopt another one, until you've adopted ~n~ cats in total. Each cat has an associated daily cost of ~c_i~ dollars for food and other essentials.

After some time, you decide to reflect on your total daily spending. You are given ~q~ queries, each with a cost threshold ~t_j~. For each query, determine the maximum number of cats you can afford, starting from the first one you adopted, such that your cumulative daily cost does not exceed the threshold.

Input

On the first line, you are given two integers ~n~ and ~q~, where ~n~ ~(1 \leq n \leq 10^5)~ is the number of cats you've adopted, and ~q~ ~(1 \leq q \leq 10^5)~ is the number of threshold queries.

On the second line, you are given ~n~ space-separated positive integers ~c_i~ ~(1 \leq c_i \leq 10^4)~, where ~c_i~ represents the cost of the ~i~th cat.

On the third line, you are given ~q~ space-separated non-negative integers ~t_j~ ~(0 \leq t_j \leq 10^9)~, where ~t_j~ represents the ~j~th threshold.

Output

For each query, print one number, each on its own line.

Examples

Input 1

4 3
2 4 3 5
2 8 1

Output 1

1
2
0

Explanation

Query 1:

• Threshold ~t_0 = 2~
• After ~1~ cat, the total daily spend is ~$2~. Thus we output ~1~ cat.

Query 2:

• Threshold ~t_1 = 8~
• After ~2~ cats, the total daily spend is ~$2 + $4 = $6~. Thus we output ~2~ cats. If we were to include the third cat, we would exceed our threshold.

Query 3:

• Threshold ~t_2 = 1~
• No number of cats will allow us to spend less than ~$1~. Thus we output ~0~.