Fibonacci Modified

I’ve been having a little fun while I’ve been keeping my programming and C# skills sharp.  Here is one of the problems I solved a little while ago.  The biggest stinker about this problem was that the numbers could get very large.  Larger than the Int64 would handle, so I had to install the BigInteger class to manage the really big numbers.  After that, the problem is pretty straight forward.

A series is defined in the following manner:

Given the n^th and (n+1)^th terms, the (n+2)^th can be computed by the following relation
T_n+2 = (T_n+1)² + T_n

So, if the first two terms of the series are 0 and 1:
the third term = 1² + 0 = 1
fourth term = 1² + 1 = 2
fifth term = 2² + 1 = 5
… And so on.

Given three integers A, B and N, such that the first two terms of the series (1^st and 2^nd terms) are A and Brespectively, compute the N^th term of the series.

Input Format

You are given three space separated integers A, B and N on one line.

Input Constraints
0 <= A,B <= 2
3 <= N <= 20

Output Format

One integer.
This integer is the N^th term of the given series when the first two terms are A and B respectively.

Note

• Some output may even exceed the range of 64 bit integer.

Sample Input

0 1 5  

Sample Output

5

Explanation

The first two terms of the series are 0 and 1. The fifth term is 5. How we arrive at the fifth term, is explained step by step in the introductory sections.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;

namespace FibonacciModified
{
	class Program
	{
		// Input Constraints 
		// 0 <= A,B <= 2 
		// 3 <= N <= 20

		static void Main(string[] args)
		{
			string[] tokens_ABN = Console.ReadLine().Split(' ');
			int A, B, N;
			BigInteger biA, biB, biN;

			A = Convert.ToInt32(tokens_ABN[0]);
			B = Convert.ToInt32(tokens_ABN[1]);
			N = Convert.ToInt32(tokens_ABN[2]);

			biA = A;
			biB = B;
			biN = 0;
			for (int i = 2; i < N; i++)
			{
				biN = (biA + (biB * biB));
				biA = biB;
				biB = biN;
			}
			Console.WriteLine(biN);
		}
	}
}