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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class Main {

    private FastScanner scanner = new FastScanner();

    public static void main(String[] args) {
        new Main().solve();
    }

    List<List<Integer>> gr = new ArrayList<>();

    private void solve() {

        int n = scanner.nextInt(), k = scanner.nextInt();
        int a[][] = new int[n][n];

        if (k > n * n) {
            System.out.println(-1);
            return;
        }


        int curi = 0, curj = 1, td = 1;

        if (k > 0) {
            a[0][0] = 1;
            k--;
            while (k > 0) {
                if (k == 1) {
                    if (a[curi][curi] != 0) {
                        curi++;
                    }
                    a[curi][curi] = 1;
                    break;
                }

                a[curi][curj] = 1;
                a[curj][curi] = 1;
                k -= 2;

                if (curi == curj) {
                    k++;
                }

                curj++;
                if (curj == n) {
                    curi++;
                    curj = curi;
                }
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                System.out.print(a[i][j] + " ");
            }
            System.out.println();
        }


    }

    public static final <T> void swap(T[] a, int i, int j) {
        T t = a[i];
        a[i] = a[j];
        a[j] = t;
    }

    class Pair implements Comparable<Pair> {
        int a, i;

        public Pair(int a, int i) {
            this.a = a;
            this.i = i;
        }

        @Override
        public int compareTo(Pair o) {
            return this.a - o.a;
        }
    }

    long gcd(long a, long b) {
        if (b != 0) {
            return gcd(b, a % b);
        }
        return a;
    }

    void initGr(int n, int m) {
        for (int i = 0; i < n; i++) {
            gr.add(new ArrayList<>());
        }

        for (int i = 0; i < m; i++) {
            int u = scanner.nextInt() - 1, v = scanner.nextInt() - 1;
            gr.get(u).add(v);
            gr.get(v).add(u);
        }
    }

    class FastScanner {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public FastScanner() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

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

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

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

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }
}