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Arrange Balls
Medium Accuracy: 72.86% Submissions: 118 Points: 4

There are p balls of type P, q balls of type Q and r balls of type R. Using the balls we want to create a straight line such that no two balls of same type are adjacent.
 

Example 1:

Input: p = 2, q = 2, r = 2
Output: 30
Explanation: There are 30 possible arrangements
of balls. Some of them are PQR, PRQ, PRP, PRQ,
PQR,...

Example 2:

Input: p = 1, q = 1, r = 1
Output: 6
Explanation: There are 6 possible arrangements
and these are PQR, PRQ, QPR, QRP, RPQ, RQP.

 

Your Task:
You don't need to read or print anything. Your task is to complete the function CountWays() which takes count of P type balls, Q type balls and R type balls and returns total number of possible arrangements such that no two balls of same type are adjacent modulo 109 + 7.

 

Expected Time Complexity: O(N3) where N = max(p, q, r)
Expected Space Complexity: O(N3)

 

Constranits: 
1 <= p, q, r <= 100 

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Arrange Balls

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