We have a grid with (2^N - 1) rows and (2^M-1) columns. You are asked to write 0 or 1 in each of these squares. Let a_{i,j} be the number written in the square at the i-th row from the top and the j-th column from the left.

For a quadruple of integers (i_1, i_2, j_1, j_2) such that 1\leq i_1 \leq i_2\leq 2^N-1, 1\leq j_1 \leq j_2\leq 2^M-1, let S(i_1, i_2, j_1, j_2) = \displaystyle \sum_{r=i_1}^{i_2}\sum_{c=j_1}^{j_2}a_{r,c}. Then, let the oddness of the grid be the number of quadruples (i_1, i_2, j_1, j_2) such that S(i_1, i_2, j_1, j_2) is odd.

Find a way to fill in the grid that maximizes its oddness.

Constraints

* N and M are integers between 1 and 10 (inclusive).

Input

Input is given from Standard Input in the following format:


N M


Output

Print numbers to write in the grid so that its oddness is maximized, in the following format:


a_{1,1}a_{1,2}\cdots a_{1,2^M-1}
a_{2,1}a_{2,2}\cdots a_{2,2^M-1}
\vdots
a_{2^N-1,1}a_{2^N-1,2}\cdots a_{2^N-1,2^M-1}


If there are multiple solutions, you can print any of them.

Example

Input

1 2


Output

111
#include<bits/stdc++.h>
#define fo(i,a,b) for(int i=(a);i<=(b);++i)
#define rv(i,a,b) for(int i=(a);i>=(b);--i)
using namespace std;
const int M = 120000;
typedef long long ll;
int n,m,k;
char s[2050][2050];
void cp(int x,int y,int len){
    fo(i,0,len-1)
        fo(j,0,len-1)
            s[x+i][y+j] = s[i][j];
}
void gen(int x){
    int len=(1<<x);
    fo(i,0,len-1)
        fo(j,0,len-1)
            s[i][j] = '0';
    s[0][0]='1';
    fo(i,1,x-1){
        cp(0, 1<<i, (1<<i)-1);
        cp(1<<i, 1<<i, (1<<i)-1);
        cp(1<<i, 0, (1<<i)-1);
        s[(1<<i)-1][(1<<i)-1] = '1';
    }
}
int main(){
    cin>>n>>m;
    gen(max(n,m));
    n=1<<n;m=1<<m;
    fo(i,0,n-2){
        s[i][m-1]='\0';
        cout<<s[i]<<endl;
    }
    return 0;
}