B'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: 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 underbrace{ sigma( sigma( ldots sigma}_{m text{ times}}(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 sum limits^n_{i=1} dfrac{1}{f(i)} is minimum possible. 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 cdot 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 cdot 10^5 . 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'...