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## C. Caterpillars

Time limit: 3.0 second
Memory limit: 64 MB
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 cm i-th caterpillar needs to rest for ti 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 — characteristics of caterpillars (1 ≤ ti ≤ 109).
In the third line there is a number q — number of moments in time, which Kirill finds interesting (1 ≤ q ≤ 106).
Remaining q lines contain one query from Kirill each. A query is described by xi — number of minutes since the start of the competition (1 ≤ xi ≤ 106).

### 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.

### Sample

inputoutput
```4
1 3 2 1
12
1
2
3
4
5
6
7
8
9
10
11
12
```
```1
2
3
2
1
2
1
2
3
2
1
0
```
Problem Author: Nikita Sivukhin (prepared by Alexey Danilyuk, Nikita Sivukhin)
Problem Source: Ural Regional School Programming Contest 2015
To submit the solution for this problem go to the Problem set: 2064. Caterpillars