Consider a board with dimensions $n \times m$. You have the option to fill each cell on the board with either a $0$ or a $1$, following the given conditions:
- The sum of values in the $i$th row should be equal to $r_i$.
- The sum of values in the $j$th column should be equal to $c_j$.
Let $S$ represent the concatenation of values on the board, starting from the top-left cell $A_{1,1}$ and moving in a row-major order to the bottom-right cell $A_{n,m}$. Find a way to fill the board such that the string $S$ is lexicographically minimum.
### Input
- The first line contains two integers $n,m$.
- The second line contains $n$ integers $r_i$.
- The third line contains $m$ integers $c_j$.
### Output
- Print $n$ lines, each line is a binary string of length $m$ denoting the board. If there is no satisfied board, print `-1`.
### Constraints
- $1 \le n, m \le 80$.
- $1 \le r_i \le m$.
- $1 \le c_j \le n$.
### Example
Input:
```
3 3
2 1 2
1 2 2
```
Output:
```
011
001
110
```
