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<cstdio>
#include<cmath>
#include<cstring>
#include<string>
#include<algorithm>
#include<queue>
#include<map>
#include<set>
#include<vector>
#include<functional>
#include <random>
#include<iostream>
#include<iomanip>
using namespace std;

int grid[1024][1024];
int grid_moto[11][1024];
int grid_honto[11][1024];

int bit_sum(int a) {
	int ret = 0;
	while (a > 0) {
		ret += a % 2;
		a = a >> 1;
	}
	return ret;
}

int main() {
	int N, M;
	int H, W;
	bool swapped = false;
	cin >> N >> M;
	if (N > M) { int swap = N; N = M; M = swap; swapped = true; }
	H = 1 << N;
	W = 1 << M;


	for (int i = 1; i < N + 1; i++) {
		for (int j = 0; j < (1 << i); j++) {
			for (int k = 0; k < W / (1 << i); k++) {
				grid_moto[i-1][j*W / (1 << i) + k] = j % 2;
			}
		}
	}
	for (int i = 0; i < H; i++) {
		for (int j = 0; j < W; j++) {
			grid[i][j] = 0;
			for (int k = 0; k < N; k++) {
				if ((i >> k) % 2 == 1) {
					grid[i][j] = grid[i][j] ^ grid_moto[k][j];
				}
			}
		}
	}

	for (int i = 0; i < H; i++) {
		for (int j = 0; j < W; j++) {
			if (i == 0 || j == 0) { grid_honto[i][j] = 0; }
			else {
				grid_honto[i][j] = grid[i][j] ^ grid[i - 1][j] ^ grid[i][j - 1] ^ grid[i - 1][j - 1];
			}
		}
	}
	if (!swapped) {
		for (int i = 1; i < H; i++) {
			for (int j = 1; j < W; j++) {
				cout << grid_honto[i][j];
			}
			cout << "\n";
		}
	}
	else {
		for (int i = 1; i < W; i++) {
			for (int j = 1; j < H; j++) {
				cout << grid_honto[j][i];
			}
			cout << "\n";
		}
	}
}