Dictionary#364

Dictionary

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Easy

In the gibberish language, there are $N$ symbols—the first $N$ Latin letters. Gibberish words use all these letters, each appearing exactly once in the word. The chief gibberish linguist has compiled a dictionary in which all possible words are listed in alphabetical order. Your task is to find the word corresponding to a given number.

Input

Given the number of letters $N$ ( $2 \leq N \leq 12$ 2 \leq N \leq 12) and the word's number $k$ ( $1 \leq k \leq N!$ 1 \leq k \leq N!).

Output

Print the gibberish word.

Examples

Example 1

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2 \leq N \leq 12

1 \leq k \leq N!