Problem: You are given matrix with n rows and n columns filled with zeroes. You should put k ones in it in such a way that the resulting matrix is symmetrical with respect to the main diagonal (the diagonal that goes from the top left to the bottom right corner) and is lexicographically maximal.

One matrix is lexicographically greater than the other if the first different number in the first different row from the top in the first matrix is greater than the corresponding number in the second one.

If there exists no such matrix then output -1.

Input

The first line consists of two numbers n and k (1 ≤ n ≤ 100, 0 ≤ k ≤ 106).

Output

If the answer exists then output resulting matrix. Otherwise output -1.

Examples

Input

2 1


Output

1 0 
0 0 


Input

3 2


Output

1 0 0 
0 1 0 
0 0 0 


Input

2 5


Output

-1

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.util.*;

public class A {
	final static int MOD = 1000000007;

	public static void main(String[] args) throws Exception {
		FastReader in = new FastReader(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		if (n * n < k) {
			System.out.println(-1);
			return;
		}
		int[][] ar = new int[n][n];
		if (k == 0) {
			printArray(ar);
			return;
		}
		int i = 0;
		while (i < n) {
			int j = i;
			ar[i][i] = 1;
			k--;
			if (k == 0) {
				printArray(ar);
				return;
			}
			for (j = i + 1; j < n; j++) {
				if (k > 1) {
					ar[j][i] = 1;
					ar[i][j] = 1;
					k -= 2;
					if (k == 0) {
						printArray(ar);
						return;
					}
				}
			}
			i++;
		}
	}

	static void printArray(int[][] ar) {
		for (int i = 0; i < ar.length; i++) {
			for (int j = 0; j < ar.length; j++)
				System.out.print(ar[i][j] + " ");
			System.out.println();
		}
	}

	static class FastReader {
	    private boolean finished = false;

	    private InputStream stream;
	    private byte[] buf = new byte[1024];
	    private int curChar;
	    private int numChars;
	    private SpaceCharFilter filter;

	    public FastReader(InputStream stream) {
	        this.stream = stream;
	    }

	    public int read() {
	        if (numChars == -1) {
	            throw new InputMismatchException();
	        }
	        if (curChar >= numChars) {
	            curChar = 0;
	            try {
	                numChars = stream.read(buf);
	            } catch (IOException e) {
	                throw new InputMismatchException();
	            }
	            if (numChars <= 0) {
	                return -1;
	            }
	        }

	        return buf[curChar++];
	    }

	    public int peek() {
	        if (numChars == -1) {
	            return -1;
	        }
	        if (curChar >= numChars) {
	            curChar = 0;
	            try {
	                numChars = stream.read(buf);
	            } catch (IOException e) {
	                return -1;
	            }
	            if (numChars <= 0) {
	                return -1;
	            }
	        }
	        return buf[curChar];
	    }

	    public int nextInt() {
	        int c = read();
	        while (isSpaceChar(c))
	            c = read();
	        int sgn = 1;
	        if (c == '-') {
	            sgn = -1;
	            c = read();
	        }
	        int res = 0;
	        do {
	            if (c == ',') {
	                c = read();
	            }
	            if (c < '0' || c > '9') {
	                throw new InputMismatchException();
	            }
	            res *= 10;
	            res += c - '0';
	            c = read();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }

	    public long nextLong() {
	        int c = read();
	        while (isSpaceChar(c))
	            c = read();
	        int sgn = 1;
	        if (c == '-') {
	            sgn = -1;
	            c = read();
	        }
	        long res = 0;
	        do {
	            if (c < '0' || c > '9') {
	                throw new InputMismatchException();
	            }
	            res *= 10;
	            res += c - '0';
	            c = read();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }

	    public String nextString() {
	        int c = read();
	        while (isSpaceChar(c))
	            c = read();
	        StringBuilder res = new StringBuilder();
	        do {
	            res.appendCodePoint(c);
	            c = read();
	        } while (!isSpaceChar(c));
	        return res.toString();
	    }

	    public boolean isSpaceChar(int c) {
	        if (filter != null) {
	            return filter.isSpaceChar(c);
	        }
	        return isWhitespace(c);
	    }

	    public static boolean isWhitespace(int c) {
	        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    }

	    private String readLine0() {
	        StringBuilder buf = new StringBuilder();
	        int c = read();
	        while (c != '\n' && c != -1) {
	            if (c != '\r') {
	                buf.appendCodePoint(c);
	            }
	            c = read();
	        }
	        return buf.toString();
	    }

	    public String nextLine() {
	        String s = readLine0();
	        while (s.trim().length() == 0)
	            s = readLine0();
	        return s;
	    }

	    public String nextLine(boolean ignoreEmptyLines) {
	        if (ignoreEmptyLines) {
	            return nextLine();
	        } else {
	            return readLine0();
	        }
	    }

	    public BigInteger nextBigInteger() {
	        try {
	            return new BigInteger(nextString());
	        } catch (NumberFormatException e) {
	            throw new InputMismatchException();
	        }
	    }

	    public char nextCharacter() {
	        int c = read();
	        while (isSpaceChar(c))
	            c = read();
	        return (char) c;
	    }

	    public double nextDouble() {
	        int c = read();
	        while (isSpaceChar(c))
	            c = read();
	        int sgn = 1;
	        if (c == '-') {
	            sgn = -1;
	            c = read();
	        }
	        double res = 0;
	        while (!isSpaceChar(c) && c != '.') {
	            if (c == 'e' || c == 'E') {
	                return res * Math.pow(10, nextInt());
	            }
	            if (c < '0' || c > '9') {
	                throw new InputMismatchException();
	            }
	            res *= 10;
	            res += c - '0';
	            c = read();
	        }
	        if (c == '.') {
	            c = read();
	            double m = 1;
	            while (!isSpaceChar(c)) {
	                if (c == 'e' || c == 'E') {
	                    return res * Math.pow(10, nextInt());
	                }
	                if (c < '0' || c > '9') {
	                    throw new InputMismatchException();
	                }
	                m /= 10;
	                res += (c - '0') * m;
	                c = read();
	            }
	        }
	        return res * sgn;
	    }

	    public boolean isExhausted() {
	        int value;
	        while (isSpaceChar(value = peek()) && value != -1)
	            read();
	        return value == -1;
	    }

	    public String next() {
	        return nextString();
	    }

	    public SpaceCharFilter getFilter() {
	        return filter;
	    }

	    public void setFilter(SpaceCharFilter filter) {
	        this.filter = filter;
	    }

	    public interface SpaceCharFilter {
	        public boolean isSpaceChar(int ch);
	    }
	}
}