P8684 - Half Turns

内存限制：128 MB 时间限制：1 S 标准输入输出

题目类型：传统评测方式：文本比较上传者：

提交：6 通过：1

Given two even integers

n

and

m

, construct a matrix

M

satisfying following constraints:

The number of rows and columns of $M$ are $n$ and $m$ respectively.
For each integer $i$ $\le i \le nm)$ , $i$ appears exactly once in $M$ .
For each two adjacent integers $i$ and $i + 1$ $\le i < nm)$ , denoting $M_{x_1,y_1} = i$ and $M_{x_2,y_2} = i+1$ , then $x_1 - x_2| + |y_1 - y_2| = 1$ holds.
The number of turning integers is exactly $nm2\frac{nm}{2}$ , where $i$ $(1 < i < n m)$ is a turning integer iff the three integers $i - 1$ , $i$ and $i + 1$ are not in the same row or the same column.

If multiple solution exist, print any one of them. If no solution exist, report it.

The only line contains two even integers  $n$  and  $m$   $\le n,m \le 1\,000)$ .

If no solution, print "No" (without quotes) in one line.
If solution exists, print "Yes" (without quotes) in the first line. Then print  $n$  lines each containing  $m$  integers  $Mi,1,Mi,2,⋯,Mi,mM_{i,1}, M_{i,2}, \cdots, M_{i,m}$ , denoting the answer matrix.

4 4

In the sample case, the number of turning integers is

8

, which equals

4×42\frac{4\times 4}{2}

, and the 8 turning integers are

2, 5, 6, 8, 9, 11, 12, 15

2022 牛客9

8684: Half Turns

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