Consider a board with dimensions n×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 ith row should be equal to ri.
- The sum of values in the jth column should be equal to cj.
Let S represent the concatenation of values on the board, starting from the top-left cell A1,1 and moving in a row-major order to the bottom-right cell An,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 ri.
- The third line contains m integers cj.
### 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≤n,m≤80.
- 1≤ri≤m.
- 1≤cj≤n.
### Example
Input:
33212122
Output:
011001110