Description:
Optimizing the amount of data transmitted via a network is an important and interesting part of developing any network application.
In one secret game developed deep in the ZeptoLab company, the game universe consists of n levels, located in a circle. You can get from level i to levels i - 1 and i + 1, also you can get from level 1 to level n and vice versa. The map of the i-th level description size is ai bytes.
In order to reduce the transmitted traffic, the game gets levels as follows. All the levels on the server are divided into m groups and each time a player finds himself on one of the levels of a certain group for the first time, the server sends all levels of the group to the game client as a single packet. Thus, when a player travels inside the levels of a single group, the application doesn't need any new information. Due to the technical limitations the packet can contain an arbitrary number of levels but their total size mustn't exceed b bytes, where b is some positive integer constant.
Usual situation is that players finish levels one by one, that's why a decision was made to split n levels into m groups so that each group was a continuous segment containing multiple neighboring levels (also, the group can have two adjacent levels, n and 1). Specifically, if the descriptions of all levels have the total weight of at most b bytes, then they can all be united into one group to be sent in a single packet.
Determine, what minimum number of groups do you need to make in order to organize the levels of the game observing the conditions above?
As developing a game is a long process and technology never stagnates, it is yet impossible to predict exactly what value will take constant value b limiting the packet size when the game is out. That's why the developers ask you to find the answer for multiple values of b.
Input Format:
The first line contains two integers n, q (2 ≤ n ≤ 106, 1 ≤ q ≤ 50) — the number of levels in the game universe and the number of distinct values of b that you need to process.
The second line contains n integers ai (1 ≤ ai ≤ 109) — the sizes of the levels in bytes.
The next q lines contain integers bj ($$\max \{a_{i}\} \leq b_{j} \leq 10^{15}$$), determining the values of constant b, for which you need to determine the answer.
Output Format:
For each value of kj from the input print on a single line integer mj (1 ≤ mj ≤ n), determining the minimum number of groups to divide game levels into for transmission via network observing the given conditions.
Note:
In the test from the statement you can do in the following manner.
- at b = 7 you can divide into two segments: 2|421|32 (note that one of the segments contains the fifth, sixth and first levels);
- at b = 4 you can divide into four segments: 2|4|21|3|2;
- at b = 6 you can divide into three segments: 24|21|32|.