Transmitting Levels

题意翻译

题意：给你一个环形数组，让你求将这个数组分成 每段和 <= k 的最小段数。

题目描述

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 $ a_{i} $ 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 $ .

输入输出格式

输入格式

The first line contains two integers $ n $ , $ q $ ( $ 2<=n<=10^{6} $ , $ 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 $ a_{i} $ ( $ 1<=a_{i}<=10^{9} $ ) — the sizes of the levels in bytes. The next $ q $ lines contain integers $ b_{j} $ (), determining the values of constant $ b $ , for which you need to determine the answer.

输出格式

For each value of $ k_{j} $ from the input print on a single line integer $ m_{j} $ ( $ 1<=m_{j}<=n $ ), determining the minimum number of groups to divide game levels into for transmission via network observing the given conditions.

输入输出样例

输入样例 #1

6 3
2 4 2 1 3 2
7
4
6

输出样例 #1

2
4
3

说明

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| $ .