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:
//package cf;
import java.io.*;
import java.util.*;

public final class Cf {

    public static void main(String[] args) throws Exception {
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(java.io.FileDescriptor.out), "ASCII"), 512);        
        Reader sc = new Reader();
        int n,k,a[][];
        n=sc.nextInt();
        k=sc.nextInt();
        a=new int[n][n];
        if(k>n*n)out.write("-1");
        else
        {
          for(int i=0;i<n&&k>0;i++)
          {
              a[i][i]=1;k--;
              for(int j=i+1;k>1&&j<n;j++)
              {
                  a[i][j]=a[j][i]=1;
                  k-=2;
              }
          }
          
          for(int v[]:a)
          {
              for(int vv:v)System.out.print(vv+" ");
              System.out.println();
          }
                           
        }
        out.flush();
        
    }
    public static void debug(String s)
    {
        System.out.println(s);
    }

    ///////////////////////////////////////////////////////////////////////////////////
    //////////////////////////////////////////////////////////////////////////////////////////////
    static class FastReader {        
        
        BufferedReader br;        
        StringTokenizer st;        
        
        public FastReader() {            
            br = new BufferedReader(new InputStreamReader(System.in));            
        }        
        
        String next() {            
            while (st == null || !st.hasMoreElements()) {                
                try {                    
                    st = new StringTokenizer(br.readLine());                    
                } catch (IOException e) {                    
                    e.printStackTrace();                    
                }                
            }            
            return st.nextToken();            
        }        
        
        int nextInt() {            
            return Integer.parseInt(next());            
        }        
        
        long nextLong() {            
            return Long.parseLong(next());            
        }        
        
        double nextDouble() {            
            return Double.parseDouble(next());            
        }        
        
        String nextLine() {            
            String str = "";            
            try {                
                str = br.readLine();                
            } catch (IOException e) {                
                e.printStackTrace();                
            }            
            return str;            
        }        
    }
    //////////////////////////////////////////////////////////////////

    static class Reader {        

        final private int BUFFER_SIZE = 1 << 16;        
        private DataInputStream din;        
        private byte[] buffer;        
        private int bufferPointer, bytesRead;        
        
        public Reader() {            
            din = new DataInputStream(System.in);            
            buffer = new byte[BUFFER_SIZE];            
            bufferPointer = bytesRead = 0;            
        }        
        
        public Reader(String file_name) throws IOException {            
            din = new DataInputStream(new FileInputStream(file_name));            
            buffer = new byte[BUFFER_SIZE];            
            bufferPointer = bytesRead = 0;            
        }        
        
        public String readLine() throws IOException {            
            byte[] buf = new byte[1002]; // line length 
            int cnt = 0, c;            
            while ((c = read()) != -1) {                
                if (c == '\n') {
                    break;
                }                
                buf[cnt++] = (byte) c;                
            }            
            return new String(buf, 0, cnt);            
        }        
        
        public int nextInt() throws IOException {            
            int ret = 0;            
            byte c = read();            
            while (c <= ' ') {
                c = read();
            }            
            boolean neg = (c == '-');            
            if (neg) {
                c = read();
            }            
            do {                
                ret = ret * 10 + c - '0';                
            } while ((c = read()) >= '0' && c <= '9');            
            
            if (neg) {
                return -ret;
            }            
            return ret;            
        }        
        
        public long nextLong() throws IOException {            
            long ret = 0;            
            byte c = read();            
            while (c <= ' ') {
                c = read();
            }            
            boolean neg = (c == '-');            
            if (neg) {
                c = read();
            }            
            do {                
                ret = ret * 10 + c - '0';                
            } while ((c = read()) >= '0' && c <= '9');            
            if (neg) {
                return -ret;
            }            
            return ret;            
        }        
        
        public double nextDouble() throws IOException {            
            double ret = 0, div = 1;            
            byte c = read();            
            while (c <= ' ') {
                c = read();
            }            
            boolean neg = (c == '-');            
            if (neg) {
                c = read();
            }            
            
            do {                
                ret = ret * 10 + c - '0';                
            } while ((c = read()) >= '0' && c <= '9');            
            
            if (c == '.') {                
                while ((c = read()) >= '0' && c <= '9') {                    
                    ret += (c - '0') / (div *= 10);                    
                }                
            }            
            
            if (neg) {
                return -ret;
            }            
            return ret;            
        }        
        
        private void fillBuffer() throws IOException {            
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);            
            if (bytesRead == -1) {
                buffer[0] = -1;
            }            
        }        
        
        private byte read() throws IOException {            
            if (bufferPointer == bytesRead) {
                fillBuffer();
            }            
            return buffer[bufferPointer++];            
        }        
        
        public void close() throws IOException {            
            if (din == null) {
                return;
            }            
            din.close();            
        }        
    }    
}