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>
#include<vector>
using namespace std;

template<class T, int base>
class RollingHash{
    vector<long long> hash, power;
    static const int mod = 1000000007;
public:
    RollingHash(const T& s){
        init(s);
    }
    
    void init(const T& s){
        int n = s.size();
        hash.assign(n+1, 0);
        power.assign(n+1, 1);
        for(int i = 0; i < n; ++i){
            hash[i+1] = (hash[i] * base + s[i]) % mod;
            power[i+1] = power[i] * base % mod;
        }
    }
    
    //S[l, r)
    long long find(const int l, const int r){
        long long res = hash[r] + mod - hash[l] * power[r-l] % mod;
        if(res >= mod){
            res -= mod;
        }
        return res;
    }
};

template<class T>
vector<vector<long long>> rectangle_hash(const vector<T>& field, const int r, const int c){
    static const long long base1 = 1007, base2 = 2009;
    vector<RollingHash<T, base1>> rh;
    for(auto s : field){
        rh.emplace_back(s);
    }
    int h = field.size();
    int w = field[0].size();

    vector<vector<long long>> res(h-r+1, vector<long long>(w-c+1));

    for(int j = 0; j+c <= w; ++j){
        vector<long long> tmp(h);
        for(int i = 0; i < h; ++i){
            tmp[i] = rh[i].find(j, j+c);
        }

        RollingHash<vector<long long>, base2> second_step(tmp);
        for(int i = 0; i+r <= h; ++i){
            res[i][j] = second_step.find(i, i+r);
        }
    }
    return res;
}

int main(){

    int h, w;
    cin >> h >> w;
    vector<string> field(h);
    for(int i = 0; i < h; ++i){
        cin >> field[i];
    }
    int r, c;
    cin >> r >> c;
    vector<string> pattern(r);
    for(int i = 0; i < r; ++i){
        cin >> pattern[i];
    }

    auto feild_hash = rectangle_hash<string>(field, r, c);
    auto pattern_hash = rectangle_hash<string>(pattern, r, c);

    for(int i = 0; i+r <= h; ++i){
        for(int j = 0; j+c <= w; ++j){
            if(feild_hash[i][j] == pattern_hash[0][0]){
                cout << i << " " << j << endl;
            }
        }
    }
    return 0;
}