P10644 [NordicOI 2022] Power Grid

Translated from Nordic Olympiad in Informatics 2022 [Power Grid](https://noi22.kattis.com/contests/noi22/problems/powergrid)。If you find that the SPJ is broken, please contact the problem porter qvq。 $\texttt{5s,1G}$。**Please do not abuse the judging of this problem.**

There is a city consisting of an $N$ by $M$ grid, with a total of $N\times M$ cells. The power consumption of cell $(i,j)$ is denoted by $A_{i,j}$。Here, $A_{i,j}$ can be positive, negative, or $0$。 For cell $(i,j)$, define $$C_{i, j} = \left| \sum _{k=1}^ N A_{k, j} - \sum _{k=1}^ M A_{i, k} \right| $$ That is, the absolute value of the difference between the total power usage of a column and the total power usage of a row。 Given all $C_{i,j}$, can you construct a valid set of $A_{i,j}$? The testdata guarantees that at least one solution exists。

The first line contains two positive integers $N, M$, with meanings as described in the statement。 In the next $N$ lines, the $j$-th number in line $i$ is $C_{i,j}$, with meaning as described in the statement。 It is guaranteed that at least one solution exists。

Output $N$ lines each with $M$ numbers, where the $j$-th number in line $i$ is $A_{i,j}$。 If there are multiple solutions, output any one of them。 You need to ensure that $-2^{31}\le A_{i,j}\lt 2^{31}$。

#### Constraints - $1\le N, M\le 1\, 000$； - $0\le C_{i,j}\le 1\, 000$； - At least one solution is guaranteed。 #### Subtasks | Subtask ID | Score | Constraints | | :--: | :--: | :--: | | $1$ | $8$ | $N, M, C_{i,j}\le 3$ | | $2$ | $5$ | $N, M, C_{i,j}\le 6$ | | $3$ | $11$ | $N=1$ | | $4$ | $6$ | $N, M\ge 2$，all $C_{i,j}$ are the same | | $5$ | $15$ | $N, M\ge 2$，all $C_{i,j}$ are pairwise distinct | | $6$ | $5$ | $C_{i,j}\le 1$ | | $7$ | $15$ | $N=M$ | | $8$ | $25$ | $N, M, C_{i,j}\le 100$ | | $9$ | $10$ | No additional constraints | Translated by ChatGPT 5