AtCoder Grand Contest 016
C
+/- Rectangle
AtCoder
⌀ 2017
原题
← BD →
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Problem Statement

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You are given four integers: $H$, $W$, $h$ and $w$ ($1 ≤ h ≤ H$, $1 ≤ w ≤ W$). Determine whether there exists a matrix such that all of the following conditions are held, and construct one such matrix if the answer is positive:

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  • The matrix has $H$ rows and $W$ columns.
  • Each element of the matrix is an integer between $-10^9$ and $10^9$ (inclusive).
  • The sum of all the elements of the matrix is positive.
  • The sum of all the elements within every subrectangle with $h$ rows and $w$ columns in the matrix is negative.
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Constraints

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  • $1 ≤ h ≤ H ≤ 500$
  • $1 ≤ w ≤ W ≤ 500$
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Input

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Input is given from Standard Input in the following format:

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H W h w

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Output

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If there does not exist a matrix that satisfies all of the conditions, print No.

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Otherwise, print Yes in the first line, and print a matrix in the subsequent lines in the following format:

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a_{11} ... a_{1W}
:
a_{H1} ... a_{HW}

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Here, $a_{ij}$ represents the $(i,\ j)$ element of the matrix.

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样例

Input #1
3 3 2 2
Output #1
Yes
1 1 1
1 -4 1
1 1 1
The sum of all the elements of this matrix is $4$, which is positive. Also, in this matrix, there are four subrectangles with $2$ rows and $2$ columns as shown below. For each of them, the sum of all the elements inside is $-1$, which is negative. ![bbdb651fa1f05996886da9f0c4d8090a.png](https://atcoder.jp/img/agc016/bbdb651fa1f05996886da9f0c4d8090a.png)
Input #2
2 4 1 2
Output #2
No
Input #3
3 4 2 3
Output #3
Yes
2 -5 8 7
3 -5 -4 -5
2 1 -1 7
题目信息
题号
agc016_c
时间限制
2 s
内存限制
256 MB

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