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 static java.lang.Double.parseDouble;
import static java.lang.Integer.max;
import static java.lang.Integer.min;
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.StrictMath.abs;
import static java.lang.System.exit;
import static java.util.Arrays.sort;
import java.io.*;
import java.util.*;


public class A {

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;

    static void solve() throws Exception {
        int n = nextInt(), k = nextInt();
        int a[][] = new int[n][n];
        if(k > n * n) {
            out.print(-1);
            return;
        }
        for(int i=0;i<n;i++) Arrays.fill(a[i],0);
        int i = 0,j = 0;
        while( k > 0 ) {
            if(k == 1) {
                if(j!=0) i++;
                a[i][i] = 1;
                k--;
            } else {
                if(a[i][j] == 1) {
                    j++;
                    if(j == n) {
                        j = 0;
                        i++;
                        if(i == n) break;
                    }
                    continue;
                }
                a[i][j] = a[j][i] = 1;
                if(i == j) k--;else k -= 2;
                j++;
                if(j == n) {
                    j = 0;
                    i++;
                    if(i == n) break;
                }
            }
        }
        for(int x=0;x<n;x++)
            for (int y=0;y<n;y++) if(a[x][y] != a[y][x]) {
                out.print(-1);
                return;
            }
        for(int x=0;x<n;x++) {
            for (int y=0;y<n;y++) out.print(a[x][y] + " ");
            out.println();
        }
    }

    public static class SegmentTreeRMQL {
        public int M, H, N;
        public long[] st;

        public SegmentTreeRMQL(int n)
        {
            N = n;
            M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
            H = M>>>1;
            st = new long[M];
            Arrays.fill(st, 0, M, Long.MAX_VALUE);
        }

        public SegmentTreeRMQL(long[] a)
        {
            N = a.length;
            M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
            H = M>>>1;
            st = new long[M];
            for(int i = 0;i < N;i++){
                st[H+i] = a[i];
            }
            Arrays.fill(st, H+N, M, Long.MAX_VALUE);
            for(int i = H-1;i >= 1;i--)propagate(i);
        }

        public void update(int pos, long x)
        {
            st[H+pos] = x;
            for(int i = (H+pos)>>>1;i >= 1;i >>>= 1)propagate(i);
        }

        private void propagate(int i)
        {
            st[i] = Math.min(st[2*i], st[2*i+1]);
        }

        public long minx(int l, int r){
            long min = Long.MAX_VALUE;
            if(l >= r)return min;
            while(l != 0){
                int f = l&-l;
                if(l+f > r)break;
                long v = st[(H+l)/f];
                if(v < min)min = v;
                l += f;
            }

            while(l < r){
                int f = r&-r;
                long v = st[(H+r)/f-1];
                if(v < min)min = v;
                r -= f;
            }
            return min;
        }

        public long min(int l, int r){ return l >= r ? 0 : min(l, r, 0, H, 1);}

        private long min(int l, int r, int cl, int cr, int cur)
        {
            if(l <= cl && cr <= r){
                return st[cur];
            }else{
                int mid = cl+cr>>>1;
                long ret = Long.MAX_VALUE;
                if(cl < r && l < mid){
                    ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
                }
                if(mid < r && l < cr){
                    ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
                }
                return ret;
            }
        }

        public int firstle(int l, long v) {
            int cur = H+l;
            while(true){
                if(st[cur] <= v){
                    if(cur < H){
                        cur = 2*cur;
                    }else{
                        return cur-H;
                    }
                }else{
                    cur++;
                    if((cur&cur-1) == 0)return -1;
                    if((cur&1)==0)cur>>>=1;
                }
            }
        }

        public int lastle(int l, long v) {
            int cur = H+l;
            while(true){
                if(st[cur] <= v){
                    if(cur < H){
                        cur = 2*cur+1;
                    }else{
                        return cur-H;
                    }
                }else{
                    if((cur&cur-1) == 0)return -1;
                    cur--;
                    if((cur&1)==1)cur>>>=1;
                }
            }
        }
    }


    static int gcd(int a, int b) { return b==0 ? a : gcd(b, a%b); }


    static int nextInt() throws IOException {
        return parseInt(next());
    }

    static long nextLong() throws IOException {
        return parseLong(next());
    }

    static double nextDouble() throws IOException {
        return parseDouble(next());
    }

    static String next() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    public static void main(String[] args) {
        try {

            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
            long lStartTime = System.currentTimeMillis();
            solve();
            long lEndTime = System.currentTimeMillis();
            //System.out.println("Elapsed time in seconds: " + (double)(lEndTime - lStartTime) / 1000.0);
            in.close();
            out.close();
        } catch (Throwable e) {
            e.printStackTrace();
            exit(1);
        }
    }
}