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 <iostream>
using namespace std;
int a[2005][2005];
void solve(int x)
{
 if(x==1)
 {
  a[1][1]=1;
  return;
 }
 solve(x-1);
 int l=(1<<(x-1));
 for(int i=1;i<l;i++)
  for(int j=1;j<l;j++)
   a[i+l][j]=a[i][j+l]=a[i+l][j+l]=a[i][j];
 a[l][l]=1;
}
int main()
{
 int n,m;
 cin>>n>>m;
 solve(max(n,m));
 for(int i=1;i<(1<<n);i++)
 {
  for(int j=1;j<(1<<m);j++)
   cout<<a[i][j];
  cout<<endl;
 }
 return 0;
}