Implement a modified Fibonacci sequence using the following definition:

Given terms $t\left[i\right]$ and $t[i+1]$ where $i\in(1,\infty)$, term $t[i+2]$ is computed as:
$t_{i+2}=t_{i}+(t_{i+1})^{2}$

Given three integers, $\mbox{t1}$, $\mbox{t2}$, and $n$, compute and print the $n^{th}$ term of a modified Fibonacci sequence.

Example

$t1=0$

$t2=1$

$n=6$

$t3=0+1^2=1$
$t4=1+1^2=2$
$t5=1+2^2=5$
$t6=2+5^2=27$

Return $27$.

Function Description

Complete the fibonacciModified function in the editor below. It must return the $n^{th}$ number in the sequence.

fibonacciModified has the following parameter(s):

int t1: an integer
int t2: an integer
int n: the iteration to report

Returns

int: the $n^{th}$ number in the sequence

Note: The value of $t[n]$ may far exceed the range of a $\mbox{64}$-bit integer. Many submission languages have libraries that can handle such large results but, for those that don't (e.g., C++), you will need to compensate for the size of the result.

Input Format

A single line of three space-separated integers, the values of $\mbox{t1}$, $\mbox{t2}$, and $n$.

Constraints

$0\leq t1,t2\leq2$
$3\leq n\leq20$
$t_n$ may far exceed the range of a $\mbox{64}$-bit integer.

Sample Input
0 1 5

Sample Output
5

Explanation

The first two terms of the sequence are $t1=0$ and $t2=1$, which gives us a modified Fibonacci sequence of $\{0,1,1,2,5,27,\ldots\}$. The $5^{th}$ term is $5$.

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