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<iostream>
using namespace std;
typedef unsigned long long ull;

const ull B1 = 9973;
const ull B2 = 1000000007;

int main(){
    int h, w;
    cin >> h >> w;
    char a[h][w];
    for(int i = 0; i < h; i++)  for(int j = 0; j < w; j++)  cin >> a[i][j];
    int r, c;
    cin >> r >> c;
    char b[r][c];
    for(int i = 0; i < r; i++)  for(int j = 0; j < c; j++)  cin >> b[i][j];
    
    ull d[h][w-c+1], hash[h-r+1][w-c+1];
    ull t1 = 1;
    for(int i = 0; i < c; i++)  t1 *= B1;
    for(int i = 0; i < h; i++){
        ull tmp = 0;
        for(int j = 0; j < c; j++){
            tmp = tmp * B1 + a[i][j];
        }
        for(int j = 0; j+c <= w; j++){
            d[i][j] = tmp;
            if(j+c < w) tmp = tmp*B1 + a[i][j+c] - a[i][j]*t1;
        }
    }
    ull t2 = 1;
    for(int i = 0; i < r; i++)  t2 *= B2;
    for(int j = 0; j < w-c+1; j++){
        ull tmp = 0;
        for(int i = 0; i < r; i++){
            tmp = tmp * B2 + d[i][j];
        }
        for(int i = 0; i+r <= h; i++){
            hash[i][j] = tmp;
            if(i+r < h) tmp = tmp * B2 + d[i+r][j] - d[i][j]*t2;
        }
    }

    ull pat[r];
    for(int i = 0; i < r; i++){
        pat[i] = 0;
        for(int j = 0; j < c; j++){
            pat[i] = pat[i] * B1 + b[i][j];
        }
    }
    ull x = 0;
    for(int i = 0; i < r; i++){
        x = x * B2 + pat[i];
    }

    for(int i = 0; i < h-r+1; i++){
        for(int j = 0; j < w-c+1; j++){
            if(hash[i][j] == x){
                cout << i << " " << j << endl;
            }
        }
    }

    return 0;
}