In combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set $\{1, 2, 3, \cdots, n\}$ is a permutation (arrangement) of those numbers so that each entry is alternately greater or less than the preceding entry.
Calculate the number of the alternating permutations $p_1,p_2,\cdots,p_n$ such that $p_1 = a$ and $p_n = b$.
Input
The first line of the input contains three integers $n$, $a$ and $b$.
It is guaranteed that $2 \le n \le 2\,000$ and $1 \le a, b \le n$ and $a \ne b$.
Output
Output a single line contains a single integer, indicating the answer.
Example
Input
2000 249 662Output
979748465