Fibonacci Modified

Problem Statement

A series is defined in the following manner:

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

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 (1st and 2nd terms) are A and B respectively, compute the Nth 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 Nth term of the given series when the first two terms are A and Brespectively.

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.

import java.io.*;

import java.util.*;

import java.math.*;

public class Solution {

    public static void main(String[] args) {

        /* Enter your code here. Read input from STDIN. Print output to STDOUT. Your class should be named Solution. */

        Scanner in = new Scanner(System.in);

        BigInteger A = in.nextBigInteger();

        BigInteger B = in.nextBigInteger();

        int N = in.nextInt();

        BigInteger[] table = new BigInteger[N];

        table[0] = A;

        table[1] = B;

        for(int i=2; i<N; i++){

            table[i] = table[i-1].pow(2).add(table[i-2]);

        }

        System.out.println(table[N-1]);

    }

}