Problem: Find places where a R × C pattern is found within a H × W region. Print top-left coordinates (i, j) of sub-regions where the pattern found. The top-left and bottom-right coordinates of the region is (0, 0) and (H-1, W-1) respectively.

Constraints

* 1 ≤ H, W ≤ 1000
* 1 ≤ R, C ≤ 1000
* The input consists of alphabetical characters and digits

Input

In the first line, two integers H and W are given. In the following H lines, i-th lines of the region are given.

In the next line, two integers R and C are given. In the following R lines, i-th lines of the pattern are given.

Example

Input

4 5
00010
00101
00010
00100
3 2
10
01
10


Output

0 3
1 2

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
typedef unsigned long long ull;
ull A=9999973,B=950527;

int H,W;
char T[1005][1005];
ull t[1005][1005];
ull t2[1005][1005];
int h,w;
char U[1005][1005];


int main(){
  scanf("%d %d",&H,&W);
  for(int i=0;i<H;i++)scanf("%s",T[i]);
  scanf("%d %d",&h,&w);
  for(int i=0;i<h;i++)scanf("%s",U[i]);
  
  ull target=0;  
  for(int i=0;i<h;i++){
    ull key=0;
    for(int j=0;j<w;j++){
      key=key*B+U[i][j];
    }
    target=target*A+key;
  }

  ull C=1;
  for(int i=0;i<w;i++)C*=B;
  
  for(int i=0;i<H;i++){
    ull key=0;
    for(int j=0;j<W;j++){
      key=key*B+T[i][j];
      if(j-w>=0)key-=T[i][j-w]*C;
      t[i][j]=key;
      t2[i][j]=t[i][j];
    }
  }
  
  C=1;
  for(int i=0;i<h;i++)C*=A;
  
  for(int i=0;i<H;i++){
    for(int j=0;j<W;j++){
      if(i)t[i][j]+=t[i-1][j]*A;
      if(i-h>=0)t[i][j]-=t2[i-h][j]*C;
      if(t[i][j]==target){
        if(i-h+1>=0&&j-w+1>=0)
          printf("%d %d\n",i-h+1,j-w+1);
      }
    }
  }


  return 0;
}