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:
    
    // template : secondThread
    
    import java.io.*;
    import java.math.BigDecimal;
    import java.math.BigInteger;
    import java.util.*;
    import java.io.BufferedReader;
    import java.io.IOException;
    import java.io.InputStreamReader;
    
    
    public class main2 {
    
    
    
    
        public static void main(String[] args) {
            try {
    
    
                PrintWriter fop = new PrintWriter(System.out);
                FastScanner fsca = new FastScanner();
    
    
                int n = fsca.nextInt();
                int k= fsca.nextInt();
                int A[][] = new int[n][n] ;
    
                if (k > n*n ){
                    System.out.println(-1);
                    return;
                }
    
                for (int i = 0; i <n ; i++) {
                    if (k <= 0)
                        break;
                    for (int j = 0; j <n ; j++) {
                        if (k <= 0)
                            break;
                        if (A[i][j] == 0){
                            if (i == j){
                                k-- ;
                                A[i][j] = 1 ;
                            }
                            else {
                                if (k >=2 ){
                                    k -= 2 ;
                                    A[i][j] = 1 ;
                                    A[j][i] = 1 ;
                                }
                            }
                        }
                    }
                }
    
                for (int i = 0; i <n ; i++) {
                    for (int j = 0; j <n ; j++) {
                        fop.append(A[i][j] + " ") ;
                    }
                    fop.append("\n") ;
                }
    
    
    
    
    
    
    
    
    
    
                
    
    
                fop.flush();
                fop.close();
            } catch (Exception e) {
                return;
            }
    
    
        }
        /*-----------------------------------------------------------------------------------------------------------------------------------------------*/
    
    
        static void sieve(int n) {
            boolean[] flag = new boolean[n];
    
            for (int i = 2; i * i < n; i++) {
                if (flag[i])
                    continue;
                else
                    for (int j = i * i; j <= n; j += i) {
                        flag[j] = true;
                    }
            }
        }
    
    
        static int gcd(int a, int b) {
            if (b > a) {
                int tenp = b;
                b = a;
                a = tenp;
            }
            int temp = 0;
            while (b != 0) {
                a %= b;
                temp = b;
                b = a;
                a = temp;
            }
            return a;
        }
    
        static long gcd_long(long a, long b) {
            if (b > a) {
                long tenp = b;
                b = a;
                a = tenp;
            }
            long temp = 0;
            while (b != 0) {
                a %= b;
                temp = b;
                b = a;
                a = temp;
            }
            return a;
        }
    
    
        static final Random random = new Random();
    
        static void ruffleSort(int[] a) {
            int n = a.length;//shuffle, then sort
            for (int i = 0; i < n; i++) {
                int oi = random.nextInt(n), temp = a[oi];
                a[oi] = a[i];
                a[i] = temp;
            }
            Arrays.sort(a);
        }
    
    
        static class FastScanner {
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
            StringTokenizer st = new StringTokenizer("");
    
            String next() {
                while (!st.hasMoreTokens())
                    try {
                        st = new StringTokenizer(br.readLine());
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                return st.nextToken();
            }
    
            int nextInt() {
                return Integer.parseInt(next());
            }
    
            int[] readArray(int n) {
                int[] a = new int[n];
                for (int i = 0; i < n; i++) a[i] = nextInt();
                return a;
            }
    
            long[] readLongArray(int n) {
                long[] a = new long[n];
                for (int i = 0; i < n; i++)
                    a[i] = nextLong();
                return a;
            }
    
            long nextLong() {
                return Long.parseLong(next());
            }
        }
    
    
    }