B'You are given a permutation p of size n , as well as a non-negative integer k . You need to construct a permutation q of size n such that operatorname{inv}(q) + operatorname{inv}(q cdot p) = k {}^ dagger {}^ ddagger , or determine if it is impossible to do so. {}^ dagger For two permutations p and q of the same size n , the permutation w = q cdot p is such that w_i = q_{p_i} for all 1 <= i <= n . {}^ ddagger For a permutation p of size n , the function operatorname{inv}(p) returns the number of inversions of p , i.e. the number of pairs of indices 1 <= i < j <= n such that p_i > p_j . Each test contains multiple test cases. The first line contains an integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The description of the test cases follows. The first line of each test case contains two integers n and k ( 1 <= n <= 3 cdot 10^5, 0 <= k <= n(n - 1) ) -- the size of p and the target number of inversions. The second line of each test case contains n integers p_1, p_2, ldots, p_n ( 1 <= p_i <= n , p_i 's are pairwise distinct) -- the given permutation p . It is guaranteed that the sum of n over all test cases does not exceed 3 cdot 10^5 . For each test case, print on one line "YES" if there exists a permutation q that satisfies the given condition, or "NO" if there is no such permutation. If the answer is "YES", on the second line, print n integers q_1, q_2, ldots, q_n that represent such a satisfactory permutation q . If there are multiple such q 's, print any of them. In the first test case, we have q cdot p = [2, 1, 3] , operatorname{inv}(q) = 3 , and operatorname{inv}(q cdot p) = 1 . In the fourth test case, we have q cdot p = [9, 1, 8, 5, 7, 6, 4, 3, 2] , operatorname{inv}(q) = 24 , and'...