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:
/*
 * For the brave souls who get this far: You are the chosen ones,
 * the valiant knights of programming who toil away, without rest,
 * fixing our most awful code. To you, true saviors, kings of men,
 * I say this: never gonna give you up, never gonna let you down,
 * never gonna run around and desert you. Never gonna make you cry,
 * never gonna say goodbye. Never gonna tell a lie and hurt you.
 * 
 * And Logic is the strongest weapon. 
 *
 */
//package Coding;

import java.io.*;
import java.math.*;
import java.util.*;
import java.util.Map.Entry;

public class Coding {

    private static InputStream stream;
    private static byte[] buf = new byte[1024];
    private static int curChar;
    private static int numChars;
    private static SpaceCharFilter filter;
    private static PrintWriter pw;
    //pw.print("Case #" + i + ": ");
    //private static int infi = (int) 1e9;
    //private static final int N = 1234567;
    //private static final double MOD = 1e9 + 9;
    //Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));

    public static int soln() {
        int n = nI(), k = nI();
        if (n * n < k) {
            pw.println("-1");
            return 0;
        }
        int[][] ans = new int[n][n];
        for (int i = 0; k > 0 && i < n; i++) {
            ans[i][i] = 1;
            k--;
            for (int j = i + 1; k > 1 && j < n; j++) {
                ans[i][j] = ans[j][i] = 1;
                k -= 2;
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                pw.print(ans[i][j] + " ");
            }
            pw.println();
        }
        return 0;
    }

    public static void main(String[] args) throws FileNotFoundException {
        InputReader(System.in);
        //pw = new PrintWriter(new FileOutputStream("ans.txt"));
        //pw = new PrintWriter(new FileOutputStream("ans1.txt"));
        pw = new PrintWriter(System.out);
        soln();
        pw.close();
    }

    /*
     *********************************************************************************************
     */
    public static void InputReader(InputStream stream1) {
        stream = stream1;
    }

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

    private static boolean isEndOfLine(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }

    private static 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++];
    }

    private static void pIArr(int[] man) {
        int l = man.length;
        for (int i = 0; i < l; i++) {
            pw.print(man[i] + " ");
        }
        pw.println();
    }

    private static void pCArr(char[] man) {
        int l = man.length;
        for (int i = 0; i < l; i++) {
            pw.print(man[i] + " ");
        }
        pw.println();
    }

    private static void pLArr(long[] man) {
        int l = man.length;
        for (int i = 0; i < l; i++) {
            pw.print(man[i] + " ");
        }
        pw.println();
    }

    private static void pDArr(double[] man) {
        int l = man.length;
        for (int i = 0; i < l; i++) {
            pw.print(man[i] + " ");
        }
        pw.println();
    }

    private static double nD() {
        return Double.parseDouble(nS());
    }

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

    private static long nL() {
        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;
    }

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

    private static String nLi() {
        int c = read();
        while (isSpaceChar(c)) {
            c = read();
        }
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isEndOfLine(c));
        return res.toString();
    }

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

    private interface SpaceCharFilter {

        public boolean isSpaceChar(int ch);
    }
}