Consider a sequence of numbers a₁, a₂,..., a_n. Its cyclic shift is any sequence obtained from it by taking some (possibly none) of its starting elements and moving them to the end in the same order. In other words, it is a sequence a_k, a_k+1,..., a_n-1, a_n, a₁, a₂,..., a_k-2, a_k-1 for some k.

The smallest cyclic shift of a given sequence is its cyclic shift that is smallest lexicographically. A sequence is lexicographically smaller than another sequence of the same length if and only if it has a smaller number in the first position they differ.

Now, consider a sequence of integers a₁, a₂,..., a_n where 0 ≤ a_i ≤ m-1, where m is some fixed constant. We define to be the sequence .

Given , m and an integer k between 1 and n, output m integer numbers: the k-th element of the smallest cyclic shift of , the k-th element of the smallest cyclic shift of ,..., the k-th element of the smallest cyclic shift of .

The first line of the input file contains three integers n, m and k (, 1 ≤ k ≤ n). The second line of the input line contains n integers a₁, a₂,..., a_n (0 ≤ a_i ≤ m-1).

Output m integer numbers one per line — k-th elements of the smallest cyclic shifts of the sequences explained above.

sample input	sample output
5 6 3 1 2 1 2 3	1 2 3 5 5 0