Ural 2064 Caterpillars

Description

Young gardener didn’t visit his garden for a long time, and now it’s not very pleasant there: n caterpillars have appeared on the ground.

Kirill decided to use this opportunity to have some fun and organized a competition — “caterpillar crawl-race.”

At Kirill’s command all caterpillars start crawling from the ground to the top of a tree. But they get tired PRetty fast. After crawling ti$t_i$ cm i-th caterpillar needs to rest for ti$t_i$ minutes. During that time it slides down a bit. Crawling speed of a caterpillar is 1 cm/minute, sliding speed — also 1 cm/minute.

Kirill is very much interested to find out how high on the tree is the leading caterpillar at different moments in time.

Input

First line contains one integer n — the number of caterpillars (1 ≤ n ≤ 106).

Second line contains n integers ti$t_i$ — characteristics of caterpillars (1≤ti≤109$1/le t_i /le 10^9$).

In the third line there is a number q — number of moments in time, which Kirill finds interesting (1≤q≤106$1/le q/le 10^6$).

Remaining q lines contain one query from Kirill each. A query is described by xi$x_i$ — number of minutes since the start of the competition (1≤xi≤106$1/le x_i /le 10^6$).

Output

For every query print in a separate line one integer, that describes how high is the highest caterpillar at the given moment of time.

题意

给定 n 只毛毛虫，及 n 个数 ti$t_i$ 。对于每只毛毛虫，它们均从 0 时刻以高度 0 向上攀爬，以 1 cm/min 的速度上爬 ti$t_i$ 分钟，再以 1cm/min 的速度下滑 ti$t_i$ 分钟，再以 1 cm/min 的速度上爬 ti$t_i$ 分钟，如此往复。

之后有 q 个询问，每个询问输入一个 x ，问对每个询问给出 n 只毛毛虫在 x 时刻最高的那只毛毛虫的高度。

分析

此题可进行暴力的预处理。

由于询问的 x 最大为 106$10^6$ ，因此只需预处理出 [1,106]$[1, 10^6]$ 区间每个时刻的最高高度。

首先可以确定对于毛毛虫 i ，ti,3ti,5ti,...$t_i, 3t_i, 5t_i, ...$ 时刻它必定处在最高点，因此暴力处理每只毛毛虫在 ti,3ti,5ti,...$t_i, 3t_i, 5t_i, ...$ 时刻的高度计为 ti$t_i$ ，始终求最大值保存在 ans[ x ] 。

对于其余时刻，可视作最高点向两边的扩展，作二维坐标即斜率为 1 或 -1 。正反向分别扫描，ans[ x ] = max(ans[x], ans[x-1] -1) ， ans[ x ] = max(ans[x], ans[x+1] - 1)。

需要注意的是，对于106$10^6$ 时刻这个截止点，必须额外处理，否则可能在边界出错。

此处不得不提及神奇的 ios::sync_with_stdio(0); 否则会被卡时间。

代码