B"Yeah, we failed to make up a New Year legend for this problem. A permutation of length n is an array of n integers such that every integer from 1 to n appears in it exactly once. An element y of permutation p is reachable from element x if x = y , or p_x = y , or p_{p_x} = y , and so on. The decomposition of a permutation p is defined as follows: firstly, we have a permutation p , all elements of which are not marked, and an empty list l . Then we do the following: while there is at least one not marked element in p , we find the leftmost such element, list all elements that are reachable from it in the order they appear in p , mark all of these elements, then cyclically shift the list of those elements so that the maximum appears at the first position, and add this list as an element of l . After all elements are marked, l is the result of this decomposition. For example, if we want to build a decomposition of p = [5, 4, 2, 3, 1, 7, 8, 6] , we do the following: The New Year transformation of a permutation is defined as follows: we build the decomposition of this permutation; then we sort all lists in decomposition in ascending order of the first elements (we don't swap the elements in these lists, only the lists themselves); then we concatenate the lists into one list which becomes a new permutation. For example, the New Year transformation of p = [5, 4, 2, 3, 1, 7, 8, 6] is built as follows: We call a permutation good if the result of its transformation is the same as the permutation itself. For example, [4, 3, 1, 2, 8, 5, 6, 7] is a good permutation; and [5, 4, 2, 3, 1, 7, 8, 6] is bad, since the result of transformation is [4, 2, 3, 5, 1, 8, 6, 7] . Your task is the following: given n and k , find the k -th (lexicographically) good permutation of length n . The first line contains one integer t ( 1 <= "...