B. Expression Matrix
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

A $$$n \times m$$$ character matrix $$$a_{ij}$$$ is called a legal expression matrix if and only if it satisfies the following conditions:

  • The matrix only contains the characters '1', '+', and '*'.
  • For each line, the string formed by reading the matrix from left to right is a legal expression.
  • For each column, the string formed by reading the matrix from top to bottom is a legal expression.

The weight of a legal expression matrix is defined as the sum of the values obtained by evaluating the $$$n + m$$$ expressions formed by reading each row from left to right and each column from top to bottom.

Find the legal expression matrix of size $$$n \times m$$$ with the smallest weight. If there are multiple answers, you can output any of them.

We define a string $$$s$$$ as a legal expression as follows:

  • If $$$s = \overbrace{111\dots111}^{\text{at least one } 1}$$$, then $$$s$$$ is a legal expression.
  • If both $$$s$$$ and $$$t$$$ are legal expressions, then $$$s$$$ * $$$t$$$ is also a legal expression.
  • If both $$$s$$$ and $$$t$$$ are legal expressions, then $$$s$$$ + $$$t$$$ is also a legal expression.
Input

The input consists of a single line with two integers $$$n, m$$$ ($$$3 \leq n, m \leq 9$$$), separated by space, representing the number of rows and columns of the matrix.

Output

Output $$$n$$$ lines, each containing $$$m$$$ characters. The $$$j$$$-th character of the $$$i$$$-th line, $$$a_{ij}$$$, represents the matrix with the smallest weight.

If there are multiple answers, you can output any one of them.

Example
Input
4 4
Output
1111
1*11
11*1
1111
Note

For the given example, the weight of the matrix is $$$4488$$$, and it can be proven that there is no matrix with a smaller weight.