write a go solution for Description:
A permutation scientist is studying a self-transforming permutation a consisting of n elements a_1,a_2,ldots,a_n.

A permutation is a sequence of integers from 1 to n of length n containing each number exactly once. For example, [1], [4,3,5,1,2] are permutations, while [1,1], [4,3,1] are not.

The permutation transforms day by day. On each day, each element x becomes a_x, that is, a_x becomes a_a_x. Specifically:

- on the first day, the permutation becomes b, where b_x=a_a_x;
- on the second day, the permutation becomes c, where c_x=b_b_x;
- ldots

You're given the permutation a' on the k-th day.

Define sigma(x)=a_x, and define f(x) as the minimal positive integer m such that sigma^m(x)=x, where sigma^m(x) denotes underbracesigma(sigma(ldotssigma_mtimes(x)ldots)).

For example, if a=[2,3,1], then sigma(1)=2, sigma^2(1)=sigma(sigma(1))=sigma(2)=3, sigma^3(1)=sigma(sigma(sigma(1)))=sigma(3)=1, so f(1)=3. And if a=[4,2,1,3], sigma(2)=2 so f(2)=1; sigma(3)=1, sigma^2(3)=4, sigma^3(3)=3 so f(3)=3.

Find the initial permutation a such that sumlimits^n_i=1dfrac1f(i) is minimum possible.

Input Format:
Each test contains multiple test cases. The first line contains an integer t (1<=t<=10^4) — the number of test cases.

The first line of each test case contains two integers n and k (1<=n<=2*10^5; 1<=k<=10^9) — the length of a, and the last day.

The second line contains n integers a'_1,a'_2,ldots,a'_n (1<=a'_i<=n) — the permutation on the k-th day.

It's guaranteed that the sum of n does not exceed 2*10^5.

Output Format:
For each test case, if at least one initial a consistent with the given a' exists, print "YES", then print n integers a_1,a_2,ldots,a_n — the initial permutation with the smallest sum sumlimits^n_i=1dfrac1f(i). If there are multiple answers with the smallest sum, print any.

If there are no valid permutations, print "NO".

Note:
In the second test case, the initial permutation can be a=[6,2,5,7,1,3,4], which becomes [3,2,1,4,6,5,7] on the first day and a'=[1,2,3,4,5,6,7] on the second day (the k-th day). Also, among all the permutations satisfying that, it has the minimum sumlimits^n_i=1dfrac1f(i), which is dfrac14+dfrac11+dfrac14+dfrac12+dfrac14+dfrac14+dfrac12=3.

In the fifth test case, the initial permutation can be a=[4,2,1,3], which becomes [3,2,4,1] on the first day, [4,2,1,3] on the second day, and so on. So it finally becomes a'=[4,2,1,3] on the 8-th day (the k-th day). And it has the minimum sumlimits^n_i=1dfrac1f(i)=dfrac13+dfrac11+dfrac13+dfrac13=2.. Output only the code with no comments, explanation, or additional text.