Задача 38633. cute tables

Consider a table of size MxN, in the cells of which there are non-negative integers. We say that a table is nice if for all i the sum of the numbers in its i-th row does not exceed R_i, and for all j the sum of the numbers in its j-th column does not exceed Cj.

You are given a table Z of size MxN, in some cells of which there are already non-negative integers. Find a nice table with the maximum sum of elements such that it matches Z on those cells where Z contains numbers.

Input
The first line of the input contains numbers M and N (1 <= M, N <= 20). The next line contains M non-negative integers - R₁, R₂, ..., R_M. Next comes a line containing N non-negative integers C₁, C₂, ..., C_N. All input limits do not exceed 106. The next M lines each contain N integers that define Z. If there is no number at some place in table Z, then  -1 is in this place in the input data.

Imprint
Output the found table – M lines of N numbers. If there is no solution, print a single number -1.
 

Examples

#	Input	Output
1	2 2 1 10 1 10 -1 -1 -1 1	0 1  1 1