Description

一个直径为1/2的小球，在一个N×m的网格里面运动。 。小球运动的初始方向Xv，Yv∈{-1，0，1）。 在横向和纵向都有一些光线，问f时刻小球会碰到多少次光线。碰到两条光线的交点只计算一次。 询问次数<=10000．n，m<=100000

Format

Input

The first line of the standard input contains two integers n and m (1<=N,M<=100000) that represent the dimensions of the table. The second line contains an -character word composed of the digits 0 i 1. The -th letter of the word describes the state of the -th horizontal transmitter where 0 means that the transmitter is off and 1 means that it is on. The third line contains an M-character word that describes the state of the vertical transmitters. The fourth line of the input contains an integer k(1<=K<=10000)): the number of queries. Each of the following K lines contains five integers x,y,Xv,Yv,t(1<x<M,1<y<N,Xv,Yv属于[-1,1],1<=T<=10^9) that describe the initial position, the velocity of the ball and the duration of its movement.

Output

Your program should output exactly k lines to the standard output: the answers to the respective queries. Each answer should have the form of a single integer: the number of times the hit signal was displayed.

Samples

4 6
1010
010110
1
5 2 1 1 8

6

Limitation