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.util.*;
import java.io.*;

public class A {

	public static void solve() {
		Kattio in = new Kattio(System.in);
       	
       	int t = in.nextInt();
		int k = in.nextInt();
		if (k > t * t)
			in.println(-1);
		else {
			int tab[][] = new int[t][t];

			for (int i = 0; i < tab.length && k > 0; i++) {
				if (k - 1 >= 0) {
					tab[i][i] = 1;
					k--;
				}
				for (int j = i + 1; j < tab.length; j++) {
					if (k - 2 >= 0) {
						tab[i][j] = 1;
						tab[j][i] = 1;
						k -= 2;
					}
				}
			}
			for (int i = 0; i < tab.length; i++) {
				for (int j = 0; j < tab.length; j++) {
					in.print(tab[i][j]+" ");
				}
				if (i < tab.length - 1)
					in.println();
			}
		}

        in.flush();
        in.close();
    }


	public static void main(String args[] ) throws Exception {


        Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
            @Override
            public void run() {
                solve();
            }
        };

        t.start();
        t.join();

    }

    private static class Kattio extends PrintWriter {
 
        private BufferedReader r;
        private String line;
        private StringTokenizer st;
        private String token;
        
        public Kattio(InputStream i) {
            super(new BufferedOutputStream(System.out));
            r = new BufferedReader(new InputStreamReader(i));
        }
        public Kattio(InputStream i, OutputStream o) {
            super(new BufferedOutputStream(o));
            r = new BufferedReader(new InputStreamReader(i));
        }
 
        public boolean hasNext() {
            return peekToken() != null;
        }
 
        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
 
        public double nextDouble() { 
            return Double.parseDouble(nextToken());
        }
 
        public long nextLong() {
            return Long.parseLong(nextToken());
        }
 
        public String next() {
            return nextToken();
        }
        
        public String nextLine() {
            token = null;
            st = null;
            try {
                return r.readLine();
            } catch (IOException e) {
                return null;
            }
        }
 
        private String peekToken() {
            if (token == null) 
                try {
                    while (st == null || !st.hasMoreTokens()) {
                        line = r.readLine();
                        if (line == null) return null;
                        st = new StringTokenizer(line);
                    }
                    token = st.nextToken();
                } catch (IOException e) { }
            return token;
        }
 
        private String nextToken() {
            String ans = peekToken();
            token = null;
            return ans;
        }
    }

	public static int[] shuffle(int[] a, Random gen){ for(int i = 0, n = a.length;i < n;i++){ int ind = gen.nextInt(n-i)+i; int d = a[i]; a[i] = a[ind]; a[ind] = d; } return a; }
}