Number of Cycles

AtCoder

IDagc060_e

Time2000ms

Memory256MB

Difficulty—

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: $N$ $K$ $P_1$ $P_2$ $\cdots$ $P_N$ [samples]

Samples

Input #1

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 $f(x)+f(y)=2+1=3$.

API Response (JSON)

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    "name": "Number of Cycles",
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    "sign": "agc060_e"
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      "statement_type": "Markdown",
      "content": "In this problem, a permutation of $(1,2,\\cdots,N)$ is occasionally called just a permutation.\nFor a permutation $a=(a_1,a_2,\\cdots,a_N)$, let $f(a)$ be the number of cycles in $a$. More accurately, th...",
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      "language": "English"
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