1259. Handshakes That Don't Cross

https://leetcode.com/problems/handshakes-that-dont-cross

Description

You are given an even number of people num_people that stand around a circle and each person shakes hands with someone else, so that there are num_people / 2 handshakes total.

Return the number of ways these handshakes could occur such that none of the handshakes cross.

Since this number could be very big, return the answer mod 10^9 + 7

Example 1:

**Input:** num\_people = 2
**Output:** 1

Example 2:

**Input:** num\_people = 4
**Output:** 2
**Explanation:** There are two ways to do it, the first way is [(1,2),(3,4)] and the second one is [(2,3),(4,1)].

Example 3:

**Input:** num\_people = 6
**Output:** 5

Example 4:

**Input:** num\_people = 8
**Output:** 14

Constraints:

• 2 <= num_people <= 1000

• num_people % 2 == 0

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