Distribute Candies Among Children II
You are given two positive integers n and limit.
Return the total number of ways to distribute n candies among 3 children such that no child gets more than limit candies.
Example 1
Input
n = 5, limit = 2Output
3There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1).
Example 2
Input
n = 3, limit = 3Output
10There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0).
Constraints
- 1 <= n <= 10^6
- 1 <= limit <= 10^6