Wilbur and Strings

题意翻译

给定一张 $n\times m $ 的网格图，每个格子上都写着 $0-9$ 中的一个数。 假如当前在点 $(x,y)$，位于其上的数为 $d$，则 $(x,y)$ 必须走到 $(x+a_d,y+b_d)$。移动之前，**可以**将 $d$ 加入串 $S$ 的末尾，初始 $S$ 为空。 $q$ 组询问，每组中给定字符串 $T$，询问是否存在一个位置作为起始点，进行若干次移动后得到给定串 $T$。 $1\leq n,m,q,|a_i|,|b_i|\leq 200$，$\sum |T|\leq 1000000$。

题目描述

Wilbur the pig now wants to play with strings. He has found an $ n $ by $ m $ table consisting only of the digits from $ 0 $ to $ 9 $ where the rows are numbered $ 1 $ to $ n $ and the columns are numbered $ 1 $ to $ m $ . Wilbur starts at some square and makes certain moves. If he is at square ( $ x $ , $ y $ ) and the digit $ d $ ( $ 0<=d<=9 $ ) is written at position ( $ x $ , $ y $ ), then he must move to the square ( $ x+a_{d} $ , $ y+b_{d} $ ), if that square lies within the table, and he stays in the square ( $ x $ , $ y $ ) otherwise. Before Wilbur makes a move, he can choose whether or not to write the digit written in this square on the white board. All digits written on the whiteboard form some string. Every time a new digit is written, it goes to the end of the current string. Wilbur has $ q $ strings that he is worried about. For each string $ s_{i} $ , Wilbur wants to know whether there exists a starting position ( $ x $ , $ y $ ) so that by making finitely many moves, Wilbur can end up with the string $ s_{i} $ written on the white board.

输入输出格式

输入格式

The first line of the input consists of three integers $ n $ , $ m $ , and $ q $ ( $ 1<=n,m,q<=200 $ ) — the dimensions of the table and the number of strings to process, respectively. Each of the next $ n $ lines contains $ m $ digits from $ 0 $ and $ 9 $ giving the table itself. Then follow $ 10 $ lines. The $ i $ -th of them contains the values $ a_{i-1} $ and $ b_{i-1} $ ( $ -200<=a_{i},b_{i}<=200 $ ), i.e. the vector that Wilbur uses to make a move from the square with a digit $ i-1 $ in it. There are $ q $ lines that follow. The $ i $ -th of them will contain a string $ s_{i} $ consisting only of digits from $ 0 $ to $ 9 $ . It is guaranteed that the total length of these $ q $ strings won't exceed $ 1000000 $ .

输出格式

For each of the $ q $ strings, print "YES" if Wilbur can choose $ x $ and $ y $ in order to finish with this string after some finite number of moves. If it's impossible, than print "NO" for the corresponding string.

输入输出样例

输入样例 #1

1 1 2
0
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
0000000000000
2413423432432

输出样例 #1

YES
NO

输入样例 #2

4 2 5
01
23
45
67
0 1
0 -1
0 1
0 -1
0 1
0 -1
0 1
0 -1
0 1
0 -1
0000000000
010101011101
32232232322
44343222342444324
6767

输出样例 #2

YES
YES
YES
NO
YES

说明

In the first sample, there is a $ 1 $ by $ 1 $ table consisting of the only digit $ 0 $ . The only move that can be made is staying on the square. The first string can be written on the white board by writing $ 0 $ repeatedly. The second string cannot be written as there is no $ 2 $ on the table.