Microcircuits

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Time limit2sMemory limit1024 MB

Summary

Count the ways to draw exactly k non-crossing lines between n contacts placed on a circle, where each line joins two contacts.

Level: Medium4 of 10
Topics: Combinatorics, Math
Solved: No attempts yet

Problem

You probably know what microcircuits look like. Pay close attention to the connections. Contacts on the circuit are joined by lines. If two lines do not intersect, there is no connection between their respective contacts.

You hold a circular circuit with $n$ contacts around its border. Count the ways to draw exactly $k$ non-intersecting lines, each connecting two of the contacts.

Input

A single line contains two integers $n$ and $k$ ( $1 \le k \le n \le 40$ ).

Output

Print the required number.

Examples2

Example 1
Input
```
4 2
```
Expected output
```
2
```
Example 2
Input
```
4 3
```
Expected output
```
0
```