AT_abc416_c [ABC416C] Concat (X-th)

You are given $ N $ strings $ S_1,\ldots,S_N $ . For a sequence $ (A_1,\ldots,A_K) $ of length $ K $ where all elements are between $ 1 $ and $ N $ , inclusive, define the string $ f(A_1,\ldots,A_K) $ as $ S_{A_1}+S_{A_2}+\dots+S_{A_K} $ . Here, `+` represents string concatenation. When all $ f(A_1,\dots,A_K) $ for the $ N^K $ sequences are sorted in lexicographical order, find the $ X $ -th smallest string.

The input is given from Standard Input in the following format: > $ N $ $ K $ $ X $ $ S_1 $ $ \vdots $ $ S_N $

Output the answer.

### Sample Explanation 1 - $ f(1,1)= $ `abcabc` - $ f(1,2)= $ `abcxxx` - $ f(1,3)= $ `abcabc` - $ f(2,1)= $ `xxxabc` - $ f(2,2)= $ `xxxxxx` - $ f(2,3)= $ `xxxabc` - $ f(3,1)= $ `abcabc` - $ f(3,2)= $ `abcxxx` - $ f(3,3)= $ `abcabc` When these are sorted in lexicographical order: `abcabc`, `abcabc`, `abcabc`, `abcabc`, `abcxxx`, `abcxxx`, `xxxabc`, `xxxabc`, `xxxxxx`, the $ 6 $ -th is `abcxxx`. ### Constraints - $ 1\leq N \leq 10 $ - $ 1\leq K \leq 5 $ - $ 1\leq X \leq N^K $ - $ S_i $ is a string consisting of lowercase English letters with length at most $ 10 $ . - $ N $ , $ K $ , and $ X $ are all integers.