Problem:
Score : 300 points

Problem Statement

We have a square grid with H rows and W columns.
Snuke wants to write 0 or 1 in each of the squares.
Here, all of the following conditions have to be satisfied:

For every row, the smaller of the following is A: the number of 0s contained in the row, and the number of 1s contained in the row. (If these two numbers are equal, “the smaller” should be read as “either”.)

For every column, the smaller of the following is B: the number of 0s contained in the column, and the number of 1s contained in the column.

Determine if these conditions can be satisfied by writing 0 or 1 in each of the squares. If the answer is yes, show one way to fill the squares so that the conditions are satisfied.

Constraints

1 \leq H,W \leq 1000

0 \leq A

2 \times A \leq W

0 \leq B

2 \times B \leq H

All values in input are integers.

Input

Input is given from Standard Input in the following format:

H W A B

Output

If the conditions cannot be satisfied by writing 0 or 1 in each of the squares, print -1.

If the conditions can be satisfied, print one way to fill the squares so that the conditions are satisfied, in the following format:

s_{11}s_{12}\cdots s_{1W}
s_{21}s_{22}\cdots s_{2W}
\vdots
s_{H1}s_{H2}\cdots s_{HW}

Here s_{ij} is the digit written in the square at the i-th row from the top and the j-th column from the left in the grid.

If multiple solutions exist, printing any of them will be accepted.

Sample Input 1

3 3 1 1

Sample Output 1

100
010
001

Every row contains two 0s and one 1, so the first condition is satisfied.
Also, every column contains two 0s and one 1, so the second condition is satisfied.

Sample Input 2

1 5 2 0

Sample Output 2

01010

Solution in C++14 (Clang 3.8.0) (judge verdict: Accepted)

#include <cstdio>
#include <iostream>
#include <iomanip>
#include <functional>
#include <algorithm>
#include <string>
#include <vector>
#include <limits>
#include <numeric>
#include <queue>
#include <cmath>
#include <set>
#include <map>
#include <stack>

using namespace std;

#define INFint (1<<30)
#define BOUND 27182818284
#define MAT 2

typedef long long ll;
typedef long long int lli;
typedef pair<ll, ll> P;

ll MOD = 1000000007;
const ll INF = (1ll<<60);
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define repi(i, a, b) for(int i=int(a);i<int(b);++i)

template<class T>
bool umax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
bool umin(T &a, const T &b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}

// gcd
template<typename T>
T gcd(T a, T b) {
    if (a == 0)
        return b;
    return gcd(b % a, a);
}

int findGCD(int arr[], int n) {
    int result = arr[0];
    for (int i = 1; i < n; i++)
        result = gcd(arr[i], result);
    return result;
}

template<typename T>
T lcm(T m, T n) {
    // 引数に0がある場合は0を返す
    if ((0 == m) || (0 == n))
        return 0;
    return ((m / gcd(m, n)) * n); // lcm = m * n / gcd(m,n)
}

template<typename A, size_t N, typename T>
void Fill(A (&array)[N], const T &val) {
    fill((T *) array, (T *) (array + N), val);
}


int dx[5] = {1, 0, -1, 0};
int dy[5] = {0, 1, 0, -1};

// v.front() = -BOUND;
// v.back() = BOUND;

//struct edge{
//    int cost, to;
//
//    edge(int in_cost, int in_to){
//        cost=in_cost;
//        to=in_to;
//    }
//    bool operator<(const edge &a) const
//    {
//        return cost > a.cost;
//    }
//};
int main() {
    int H,W,A,B; cin >> H >> W >> A >> B;
    int a[1010][1010];
    Fill(a,0);

    for(int i=0; i<H; i++){
        for(int j=0; j<W; j++){
            if( (i<B && j<A)||(i>=B && j>=A) ){
                a[i][j]=1;
            }
        }
    }

    for(int i=0; i<H; i++){
        for(int j=0; j<W; j++){
            cout << a[i][j];
        }
        cout << endl;
    }
    return 0;
}