Description

Take any permutation of $1$ to $n$, and then, between every two adjacent numbers in the permutation, insert > or < according to their relative value. Among all permutations, how many permutations have exactly $k$ symbols <$? The answer is taken modulo $2015$.

Note: A permutation of $1 \sim n$ refers to a sequence in which each of the $n$ numbers from $1 \sim n$ appears exactly once.

Input Format

A single line with two integers, representing $n$ and $k$.

Output Format

A single integer representing the answer.

5 2

66

Hint

For $30\%$ of the testdata, $n \leq 10$.

For $100\%$ of the testdata, $0 \leq k < n \leq 1000$.

Translated by ChatGPT 5