Fibonacci Modified 大整數

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

import java.math.BigInteger;
import java.util.Scanner;

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 cin=new Scanner(System.in);
        int a=cin.nextInt();
        int b=cin.nextInt();
        int n=cin.nextInt();
        int k=2;
        BigInteger i = BigInteger.valueOf(a);
        BigInteger j = BigInteger.valueOf(b);
        BigInteger res ;
        while(n!=k){
            k++; 
            res=i.add(j.multiply(j));
            i=j;
            j=res;
        }
        System.out.println(j);
    }
}