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# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.IO;
using System.Net;
using System.Net.Sockets;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Threading.Tasks;
using System.Text.RegularExpressions;
using static System.Math;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using LayoutKind = System.Runtime.InteropServices.LayoutKind;
using StructLayoutAttribute = System.Runtime.InteropServices.StructLayoutAttribute;
using FieldOffsetAttribute = System.Runtime.InteropServices.FieldOffsetAttribute;

public static class P
{
    static int h;
    static int w;
    static int a;
    static int b;
    public static void Main()
    {
        h = NextInt;
        w = NextInt;
        a = NextInt;
        b = NextInt;
        for (int i = 0; i <= h; i++)
        {
            var tmp = (2 * a - w) * i - h * a + w * b;
            if (tmp % (2 * b - h) == 0)
            {
                var j = tmp / (2 * b - h);
                for (int l = 0; l < 10; l++)
                {
                    var res = Solve(i, j);
                    if (res == null) continue;
                    Console.WriteLine(string.Join("\n", res.Select(x => string.Join("", x))));
                    return;
                }
            }
        }
        Console.WriteLine("No");
    }

    static int[][] Solve(int countH, int countW)
    {
        int[][] res = Enumerable.Range(0, h).Select(_ => new int[w]).ToArray();
        int[] count = new int[w];
        for (int i = 0; i < countW; i++)
            count[i] = b;
        for (int i = countW; i < w; i++)
            count[i] = h - b;
        var rng = new Random();
        count = count.OrderBy(x => rng.Next()).ToArray();

        for (int i = 0; i < countH; i++)
        {
            int ctr = a;
            for (int j = 0; j < w; j++)
            {
                if (0 < count[j] && 0 < ctr)
                {
                    res[i][j] = 1;
                    count[j]--;
                    ctr--;
                }
            }

            if (ctr != 0)
            {
                return null;
            }
        }
        for (int i = countH; i < h; i++)
        {
            int ctr = w - a;
            for (int j = 0; j < w; j++)
            {
                if (0 < count[j] && 0 < ctr)
                {
                    res[i][j] = 1;
                    count[j]--;
                    ctr--;
                }
            }
            if (ctr != 0)
            {
                return null;
            }
        }
        if (count.Any(x => x != 0))
        {
            return null;
        }
        return res;
    }


    static readonly TextReader In = Console.In;
    static int NextInt
    {
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        get
        {
            int res = 0;
            int next = In.Read();
            int rev = 1;
            while (45 > next || next > 57) next = In.Read();
            if (next == 45) { next = In.Read(); rev = -1; }
            while (48 <= next && next <= 57)
            {
                res = res * 10 + next - 48;
                next = In.Read();
            }
            return res * rev;
        }
    }
}


[StructLayout(LayoutKind.Explicit)]
class Random
{
    [FieldOffset(0)]
    private byte __byte;
    [FieldOffset(0)]
    private sbyte __sbyte;
    [FieldOffset(0)]
    private char __char;
    [FieldOffset(0)]
    private short __short;
    [FieldOffset(0)]
    private ushort __ushort;
    [FieldOffset(0)]
    private int __int;
    [FieldOffset(0)]
    private uint __uint;
    [FieldOffset(0)]
    private long __long;
    [FieldOffset(0)]
    private ulong __ulong;

    public byte Byte { get { Update(); return __byte; } }
    public sbyte SByte { get { Update(); return __sbyte; } }
    public char Char { get { Update(); return __char; } }
    public short Short { get { Update(); return __short; } }
    public ushort UShort { get { Update(); return __ushort; } }
    public int Int { get { Update(); return __int; } }
    public uint UInt { get { Update(); return __uint; } }
    public long Long { get { Update(); return __long; } }
    public ulong ULong { get { Update(); return __ulong; } }
    public double Double { get { return (double)ULong / ulong.MaxValue; } }

    [FieldOffset(0)]
    private ulong _xorshift;

    public Random() : this((ulong)DateTime.Now.Ticks) { }
    public Random(ulong seed) { SetSeed(seed); }
    public void SetSeed(ulong seed) => _xorshift = seed * 0x3141592c0ffeeul;

    public int Next() => Int & 2147483647;
    public void Update()
    {
        _xorshift ^= _xorshift << 7;
        _xorshift ^= _xorshift >> 9;
    }
}