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+# 2929. Distribute Candies Among Children II
+from math import comb
+
+"""
+you are given two positive integers 'n' and 'limit'. return the total number
+of ways to distritube 'n' candies among 3 children such that no child gets
+more than 'limit' candies.
+"""
+
+
+class Solution(object):
+ def distributeCandies(self, n, limit):
+ """
+ :type n: int
+ :type limit: int
+ :rtype: int
+ """
+ ans = (n + 2) * (n + 1) // 2
+ for i in range(1, 4):
+ if n - i * (limit + 1) < 0:
+ break
+ ans += (
+ (-1) ** i
+ * comb(3, i)
+ * (n - i * (limit + 1) + 2)
+ * (n - i * (limit + 1) + 1)
+ // 2
+ )
+ return ans
+
+
+if __name__ == "__main__":
+ obj = Solution()
+ print(obj.distributeCandies(n=5, limit=2))
+ print(obj.distributeCandies(n=3, limit=3))