Story

At Christmas in the Kingdom of Y.Y., there is a custom of treating part of the road network as a Christmas tree and lighting up the entire town in sequence. Every year, Christmas trees of various colors and shapes have been made on the road network. This year, the people want to skillfully combine parts of past Christmas trees to make a rainbow-shining Christmas Tree.

Problem Statement

There are $N$ vertices with distinct numbers from $1$ to $N$. On these vertices, you are given $K$ directed spanning trees rooted at vertex $1$ and $(N - 1 - K)$ directed spanning trees rooted at vertex $N$. Determine whether it is possible to make a directed spanning tree by choosing exactly $1$ edge from each of these $(N - 1)$ directed spanning trees, and if it is possible, show one example.

Input

$N\ \ K$
$P_{1, 1} \ \ P_{1, 2} \ \cdots \ P_{1,N}$
$\ \ \vdots$
$P_{N-1, 1} \ \ P_{N-1, 2} \ \cdots \ P_{N-1,N}$

• $2 \le N \le 1000$
• $0 \le K \le N - 1$
• $0 \le P_{i,j} \le N$ and $P_{i,j} \neq j$ $(1 \le i \le N - 1,\ 1 \le j \le N)$
• $P_{i,1} = 0$ $(1 \le i \le K)$
• $P_{i,N} = 0$ $(K + 1 \le i \le N - 1)$
• For each $i$ $(1 \le i \le N - 1)$, $P_{i,j}$ $(1 \le j \le N)$ defines the $i$-th directed spanning tree in the following way:
  if $P_{i,j} = 0$, vertex $j$ is the root; otherwise, the unique edge entering vertex $j$ is $P_{i,j} \to j$, which starts at $P_{i,j}$.

Output

If it is impossible to make a directed spanning tree by choosing exactly $1$ edge from each of the $(N - 1)$ directed spanning trees, print No.

If it is possible, print Yes on the $1$st line, and print one example of such a directed spanning tree on the $2$nd line in the following format. If there are multiple correct answers, any of them will be accepted.

$Q_1 \ \ Q_2 \ \cdots \ Q_N$

• $(Q_1, Q_2, \dots, Q_N)$ is a permutation of $(0, 1, \dots, N - 1)$.
• If $Q_j \neq 0$, then $P_{Q_j, j} \neq 0$.
• $Q_j$ $(1 \le j \le N)$ defines a directed spanning tree in the following way:
  if $Q_j = 0$, vertex $j$ is the root; otherwise, the unique edge entering vertex $j$ is $P_{Q_j, j} \to j$, chosen from the $Q_j$-th directed spanning tree.

Sample

3 1
0 1 2
2 3 0

Yes
2 0 1

7 6
0 1 1 2 6 2 5
0 3 7 1 1 5 1
0 4 1 1 1 4 2
0 1 5 2 1 4 3
0 1 2 1 1 1 6
0 4 6 1 4 4 4

Yes
0 5 4 1 2 3 6