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.util.*;

public class B {

    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = sc.nextInt(), k = sc.nextInt();
        int mat [][] = new int[n][n];
        main : for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (k == 0) break main;
                if (mat[i][j] == 0) {
                    if (i == j) {
                        mat[i][j] = 1;
                        k--;
                    } else {
                        if (k > 1) {
                            k-= 2;
                            mat[i][j] = 1;
                            mat[j][i] = 1;
                        }
                    }
                }
            }
        }

        if (k == 0) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (j > 0) out.print(" ");
                    out.print(mat[i][j]);
                }
                out.println();
            }
        } else {
            out.println(-1);
        }
        out.flush();
        out.close();
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner (FileReader f) {br = new BufferedReader(f);}

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }
}