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 debug(...) fprintf(stderr,__VA_ARGS__)
#define fi first
#define se second
#define MK make_pair
#define PB push_back
using namespace std;

typedef long long LL;
typedef pair<int ,int> PII;

inline int f(int i,int j){return __builtin_popcount(i|j)&1;}
int main(){
	#ifdef che
	freopen("input.txt","rt",stdin);
	freopen("output.txt","wt",stdout);
	#endif
	int n,m;scanf("%d%d", &n ,&m);
	for (int i=1;i<1<<n;++i, puts(""))
		for (int j=1; j<1<<m; ++j)putchar('0'+(f(i,j)^f(i-1,j)^f(i,j-1)^f(i-1,j-1)));
	return 0;
}