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.awt.Point;
import java.io.*;
public class Solutions {
 
	static FastScanner scr=new FastScanner();
	static PrintStream out;
	static ArrayList<ArrayList<Integer>>list=new ArrayList<ArrayList<Integer>>();
	public static void main(String[] args) {
		int n=read();
		int k=read();
		if(k>n*n) {
			System.out.println(-1);
			return;
		}
		int [][]a=new int[n][n ];
		for(int i=0;i<n  ;i++) {
			for(int j=0;j<n ;j++) {
				if(i==j && k>=1 && a[i][j]==0) {
					a[i][j]=1;
					k--;
				}else if(k>=2 && a[i][j]==0){
					a[i][j]=1;
					a[j][i]=1;
					k-=2;
				}
			}
		}
		for(int i=0;i<n;i++) {
			for(int j=0;j<n;j++) {
				 System.out.print(a[i][j]+" ");
			}
			println();
		}
	}
	static ArrayList<Integer>sort(ArrayList<Integer>ele){
		Collections.sort(ele);
		return ele;
	}
	static void print(int ele) {
		System.out.print(ele+" ");
	}static void print(String ele) {
		System.out.print(ele+" ");
	}
	static void println(int ele) {
		System.out.println(ele);
	}static void println(String ele) {
		System.out.println(ele);
	}
	static void println(){
		System.out.println();
	}
	static long pow(long base,int k,long mod) {
		long ans=1;
		for(int i=0;i<k;i++) {
			ans*=base;
			ans%=mod;
		}
		return ans;
	}
	static  int read() {
		return scr.nextInt();
	}
	static int gcd(int a,int b) {
		if(b==0) {
			return a;
		}
		return gcd(b,a%b);
	}
	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 nextLong() {
			return Long.parseLong(next());
		}
	}
	static int MAX=Integer.MAX_VALUE;
	static int MIN=Integer.MIN_VALUE;
}class triplet{
	int x;
	int y;
	int z;
	triplet(int fisrt,int second,int third){
		this.x=fisrt;
		this.y=second;
		this.z=third;
	}
	public static void add(triplet triplet) {
		// TODO Auto-generated method stub
		
	}
}
class pair{
	int x=0;
	int y=0;
	pair(int first,int second){
		this.x=first;
		this.y=second;
	}
}