[USACO 2013 Dec G]The Bessie Shuffle
题号：NC24425
时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 32 M，其他语言64 M
64bit IO Format: %lld

题目描述

Bessie is practicing her card tricks. She has already mastered the Bessie- shuffle -- a shuffle on M (2 <= M <= 100,000) cards that reorganizes the cards so the i-th card from the top is now the P[i]-th card from the top. 
Now Bessie is practicing shuffles on larger decks. She has a deck of N cards (M <= N <= 1,000,000,000) conveniently labeled 1 to N. She shuffles this deck by taking the first M cards and performing the Bessie-shuffle on them, placing the shuffled cards back on top of the deck. She then removes the top card from the deck and places it face down. She repeats this process, placing the top cards successively on top of each other, until she is out of cards. When Bessie has less than M cards left, she no longer performs the Bessie-shuffle, but continues to place the top card on top of the others. 
Bessie knows that the deck initially started in sorted order, with 1 on top, 2 next, and N on the bottom. Given the description of the Bessie-shuffle, help Bessie compute which cards end up located at Q different specified positions (1 <= Q <= N, Q <= 5,000) in the deck. 
50% of test cases will have N <= 100,000.

输入描述:

* Line 1: A single line containing N, M and Q separated by a space.

* Lines 2..1+M: Line i+1 indicates the position from the top, P[i], of
the i-th card in the Bessie-shuffle (1 <= P[i] <= M).

* Lines 2+M..1+M+Q: Line i+1+M contains a single integer q_i
describing the i-th query.  You are to compute the label on
the card located in position q_i from the top (1 <= q_i <= N).

输出描述:

* Lines 1..Q: On the i-th line, print a single integer indicating the
card at position q_i from the top.
示例1

输入

复制 
5 3 5
3
1
2
1
2
3
4
5

输出

复制 
4
5
3
1
2

说明

INPUT DETAILS:
Bessie has a deck of 5 cards initially ordered as [1, 2, 3, 4, 5].  Her
shuffle is on 3 cards and has the effect of moving the top card to the
bottom.  There are 5 queries querying each position in the deck.

OUTPUT DETAILS:
The shuffle proceeds as:
[1, 2, 3, 4, 5] -> [2, 3, 1, 4, 5] (put 2 face down)
[3, 1, 4, 5] -> [1, 4, 3, 5] (put 1 face down)
[4, 3, 5] -> [3, 5, 4] (put 3 face down)
[5, 4] (put 5 face down)
[4] (put 4 face down)
This produces the final order of [4, 5, 3, 1, 2]