Problem Statement

In this problem, a permutation of $(1,2,\\cdots,N)$ is occasionally called just a permutation.

For a permutation $a=(a_1,a_2,\\cdots,a_N)$, let $f(a)$ be the number of cycles in $a$. More accurately, the value of $f(a)$ is defined as follows.

• Consider an undirected graph consisting of $N$ vertices numbered $1$ to $N$. For each $1 \\leq i \\leq N$, add an edge connecting vertex $i$ and vertex $a_i$. Then, let $f(a)$ be the number of connected components in this graph.

You are given a permutation $P=(P_1,P_2,\\cdots,P_N)$ and an integer $K$. Determine whether there is a permutation $x$ that satisfies the following condition, and construct one if it exists.

• Let $y_i=P_{x_i}$ to define a permutation $y$.
• Then, $f(x)+f(y)=K$ holds.

For each input file, solve $T$ test cases.

Constraints

• $1 \\leq T \\leq 10^5$
• $2 \\leq N \\leq 2 \\times 10^5$
• $2 \\leq K \\leq 2N$
• $(P_1,P_2,\\cdots,P_N)$ is a permutation of $(1,2,\\cdots,N)$.
• In each input file, the sum of $N$ does not exceed $2 \\times 10^5$.
• All numbers in the input are integers.

Input

The input is given from Standard Input in the following format:

$T$ $case_1$ $case_2$ $\\vdots$ $case_T$

Each case is in the following format:

$N$ $K$ $P_1$ $P_2$ $\\cdots$ $P_N$

Output

For each case, if no permutation $x$ satisfies the condition, print No. Otherwise, print your answer in the following format:

Yes $x_1$ $x_2$ $\\cdots$ $x_N$

Each character in Yes or No in the output may be either uppercase or lowercase. If multiple solutions exist, any of them will be accepted.

Sample Input 1

3
3 3
1 3 2
2 2
2 1
4 8
1 2 3 4

Sample Output 1

Yes
2 1 3
No
Yes
1 2 3 4

In the first case, letting $x=(2,1,3)$ makes $y=(3,1,2)$, satisfying $f(x)+f(y)=2+1=3$.