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 Main {

	public static final boolean fileIO = false;
	public static final int INF = 0x7FFFFFFF;
	public static final int EPS = (int)1e9 + 7;

	public static void main(String args[]) throws IOException {
		InputStream is = null;
		OutputStream os = null;
		if (fileIO) {
			is = new FileInputStream("input.txt");
			os = new FileOutputStream("output.txt");
		} else {
			is = System.in;
			os = System.out;
		}
		InputReader in = new InputReader(is);
		PrintWriter out = new PrintWriter(os);
		//
		new Task_A().solve(in, out);
		//
		out.close();

	}




	static class Task_A {



		public void solve(InputReader in, PrintWriter out) {
			int n = in.nextInt();
			int k = in.nextInt();
			if (k > n * n) {
				out.println("-1");
			} else {
				int a[][] = new int[n][n];
				for (int i = 0; i < n; i++) {
					for (int j = i; j < n; j++) {
						if (i == j && k > 0) {
							a[i][j] = 1;
							k--;
						} else if (i != j && k > 1) {
							a[i][j] = 1;
							a[j][i] = 1;
							k -= 2;
						}
					}
				}
				//
				for (int row[] : a) {
					for (int v : row)
						out.print(v + " ");
					out.println();
				}

			}
		}
	}

	static class Task_B {

		public void solve(InputReader in, PrintWriter out) {
			int n = in.nextInt();
			Integer a[] = in.nextIntArray(n);
			//
			Integer d[] = new Integer[n];
			Arrays.fill(d, INF);
			Queue< Integer > q = new LinkedList<>();
			for (int i = 0; i < a.length; i++) {
				if (a[i] == 0) {
					q.add(i);
				}
			}
			//
			for (int i = 0; i < n; i++) {
				int f = INF;
				if (!q.isEmpty()) f = q.poll();
				while (i <= f && i < n) {
					if (i > 0) d[i] = d[i - 1] + 1;
					d[i] = Math.min(d[i], f - i);
					i++;
				}
				i--;
			}
			//
			for (int v : d) out.print(v + " ");
			out.println();
		}
	}


	static class InputReader {

		private StringTokenizer tokenizer;
		private BufferedReader reader;

		public InputReader(InputStream is) {
			tokenizer = null;
			reader = new BufferedReader(new InputStreamReader(is), 32768);
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					String line = reader.readLine();
					tokenizer = new StringTokenizer(line); // ' ' -> delimiter
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public Integer nextInt() { return Integer.parseInt(next()); }
		public Integer[] nextIntArray(int n) {
			int i = 0;
			Integer ret[] = new Integer[n];
			while (i < n) ret[i++] = nextInt();
			return ret;
		}

		public Long nextLong() { return Long.parseLong(next()); }
		public Long[] nextLongArray(int n) {
			int i = 0;
			Long ret[] = new Long[n];
			while (i < n) ret[i++] = nextLong();
			return ret;
		}
	}

}