시간 제한 | 메모리 제한 | 제출 | 정답 | 맞힌 사람 | 정답 비율 |
---|---|---|---|---|---|
1 초 (추가 시간 없음) | 1024 MB | 1 | 0 | 0 | 0.000% |
You have an $N$ by $N$ grid board, which is initially empty. You will write an integer to each cell, using each integer from $1$ to $N^2$ exactly once. Let $M_{i,j}$ be the integer written on the cell in the $i$-th row from the top and the $j$-th column from the left.
Let's define sequences $A$ and $B$ as follows:
For example, when the board looks like this,
1 3 4 2 7 6 9 8 5
$A$ and $B$ are defined as follows.
You are given integers $N, X, Y$. Find a way to fill in the cells so that the inversion numbers of $A$ and $B$ are $X$ and $Y$ respectively, or report that it is impossible to do so.
Note: an inversion number of a sequence $C = c_1, c_2, \dots, c_{N \times N}$ is the number of pairs $(i, j)$ s.t. both $i < j$ and $c_i > c_j$ are satisfied.
Input is given from Standard Input in the following format:
$N$ $X$ $Y$
If there is no solution, print 'No
'.
Otherwise, print the answer in the following format:
Yes
$M_{1,1}$ $M_{1,2}$ $\dots$ $M_{1,N}$
$M_{2,1}$ $M_{2,2}$ $\dots$ $M_{2,N}$
$\vdots$
$M_{N,1}$ $M_{N,2}$ $\dots$ $M_{N,N}$
If there are multiple solutions, you can print any of them.
3 8 13
Yes 1 3 4 2 7 6 9 8 5