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.*;
import java.util.*;
import java.math.*;
import java.lang.*;
import static java.lang.Math.*;
 
public class Sol
{
    
    static long mod=1000000007;
    
    static int a[];
    
    static void initialize(int n)
    {
        for(int i=0;i<=n;i++)
            a[i]=i;
    }
    
    static int root(int r)
    {
        while(r!=a[r])
            r=a[r];
        
        return r;
    }
    
    static void union(int u,int v)
    {
        int r1=root(u);
        int r2=root(v);
        
        a[r1]=r2;
    }
    
    
    public static void main(String args[]) throws Exception
    {
        InputReader in;
        PrintWriter w;
        boolean online = false;
        String fileName = "input";

        if (online) 
        {
            in = new InputReader(new FileInputStream(new File(fileName + ".in")));
            w = new PrintWriter(new FileWriter("out.txt"));
        } 
        else 
        {
            in = new InputReader(System.in);
            w = new PrintWriter(System.out);
        }





            int n=in.nextInt();
            int k=in.nextInt();
            int a[][]=new int[n][n];
            
            
            int rem=k;
            int i=1;
            int j=0;
            int flag=0;
        /*while(rem>0)
            {
                
                
                if(rem%2!=0){
                    if(a[j][j]==0){
                    a[j][j]=1;
                    rem--;

}
}
                else{
                    if(a[i][j]==0){
                    a[i][j]=1;
                    a[j][i]=1;
                    i++;
                    rem=rem-2;
                    }                    
                }
                
                if(i==n){
                    i=j;
                    j=i+1;
                    
                }
                if(i==n&&j==n){
                    flag=1;
                    break;
                }
                
                
            }*/
            
            if(k==0){
                    for(int it=0;it<n;it++){
                for(int jt=0;jt<n;jt++){
                    w.print(a[it][jt]+" ");
                }
                w.println();
            }
        
            }
            else{
            out:
            for(i=0;i<n;i++){
                
                for( j=0;j<n;j++){
                    
                    
                 if(i==j&&a[i][j]==0){
                        if(k%2!=0){
                            k--;
                            a[i][j]=1;
                        }
                        else{
                            
                            
                            if(i!=n&&j!=n)
                            {
                                k--;
                                a[i][j]=1;
                            }
                            
                        }
                    }
                    else if(a[i][j]==0&&i!=j&&k>1){
                        a[i][j]=1;
                        a[j][i]=1;
                        if(j==i)k--;
                        else
                        k=k-2;
                    }
                    //System.out.println(i+" "+j+" "+k);
                    
                   if(k==0)break out; 
                }
                
            }
            if(k==0){
            for(int it=0;it<n;it++){
                for(int jt=0;jt<n;jt++){
                    w.print(a[it][jt]+" ");
                }
                w.println();
            }
            }
            else{
            w.println(-1);

}
            }
        w.close();
    }
    
    
    private static long gcd(long a, long b)
    {
        while (b > 0)
        {
            long temp = b;
            b = a % b; // % is remainder
            a = temp;
        }
        return a;
    }
 
    private static long gcd(long[] input)
    {
        long result = input[0];
        
        for(int i = 1; i < input.length; i++) 
            result = gcd(result, input[i]);
        
        return result;
    }
    
    private static long lcm(long a, long b)
    {
        return a * (b / gcd(a, b));
    }
 
    private static long lcm(long[] input)
    {
        long result = input[0];
        
        for(int i = 1; i < input.length; i++) 
            result = lcm(result, input[i]);
        
        return result;
    }
    
    public static void Array_2dsort(Integer[][] a)
    {
        Arrays.sort(a, new Comparator<Integer[]>() 
        {
            public int compare(Integer[] int1, Integer[] int2) 
            {
                Integer numOfKeys1 = int1[1];       //about which column u want to sort
                Integer numOfKeys2 = int2[1];
                return numOfKeys1.compareTo(numOfKeys2);
            }
        });
    }
     
    static long powmod(long x,long n,long m)        //(a/b)%mod = (a * (b^(m-2))%mod  here --> x=a, n=mod-2, m=mod  
    {
	if (n == 0)
            return 1;
        else if (n%2==0)
            return powmod(((x%m)*(x%m))%m,n/2,m);
	else if(n%2==1)
            return (((x%m)*powmod(((x%m)*(x%m))%m,(n-1)/2,m))%m);
	else
            return 0;
    }
        
	
	static class InputReader
	{
	
                private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		
		public InputReader(InputStream stream)
		{
			this.stream = stream;
		}
		
		public int read()
		{
			if (numChars==-1) 
				throw new InputMismatchException();
			
			if (curChar >= numChars)
			{
				curChar = 0;
				try 
				{
					numChars = stream.read(buf);
				}
				catch (IOException e)
				{
					throw new InputMismatchException();
				}
				
				if(numChars <= 0)				
					return -1;
			}
			return buf[curChar++];
		}
	 
		public String nextLine()
		{
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
		}
		public int nextInt()
		{
			int c = read();
			
			while(isSpaceChar(c)) 
				c = read();
			
			int sgn = 1;
			
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			
			int res = 0;
			do 
			{
				if(c<'0'||c>'9') 
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c)); 
			
			return res * sgn;
		}
		
		public long nextLong() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			long res = 0;
			
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c));
				return res * sgn;
		}
		
		public double nextDouble() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') 
			{
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') 
			{
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) 
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, nextInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
		
		public String readString() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isSpaceChar(c));
			
			return res.toString();
		}
	 
		public boolean isSpaceChar(int c) 
		{
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	 
		public String next() 
		{
			return readString();
		}
		
		public interface SpaceCharFilter 
		{
			public boolean isSpaceChar(int ch);
		}
	}
    
}