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문제

There is a pack of cards on the table, containing n cards placed one on another. Each card has a positive integer written on one side and nothing on the other. On the top card the number 1 is written, on the second from top number 2, etc., and on the bottom card the number n is written. In the beginning all the cards in the pack are placed so that numbers are facing up. Archibald makes m turns. In the i-th turn he takes the upper ki cards, holding them together turns them upside down and places back on top of the pack. Your task is to write a program that determines the place and state of a card (upside up or down) in the pack after m moves made by Archibald!

입력

The first line of the standard input contains two positive integers – n (the number of cards in the pack, n≤100000) and m (the number of turns done by Archibald, m≤1000) – which are separated using a space symbol. Each of the following m lines contains one positive integer ki (1≤ki≤n) – the number of cards used in each turn.

The next line of the standard input contains one positive integer s (s≤10000) – the number of cards, the final position and state of which must be determined. Each of the following s lines contains one positive integer – the number written on the card, the final position and state of which must be determined. 

출력

The standard output must contain excatly s lines. Each line must contain one integer. If in the end the p-th card has the number that the m+i+1st line of the standrard input contains, the i-th line of the output file must contain the number

  • +p if the card has its number written on the side facing up or
  • -p if the card has its number written on the side facing down. 

예제 입력

8 3
1
8
4
5
4
8
1
5
2

예제 출력

-5
+4
+8
+1
-7

힌트