GCD of Fibonacci Numbers

You are given two non-negative integers a and b. Your task is to compute the Fibonacci number corresponding to the greatest common divisor (GCD) of a and b. That is, you need to compute:

$$ Fib(\gcd(a, b)) $$

This is based on the property:

$$ \gcd(\text{Fib}(a), \text{Fib}(b)) = \text{Fib}(\gcd(a, b)) $$

where Fib(n) denotes the nth Fibonacci number, defined as:

$$ Fib(0)=0, \quad Fib(1)=1, \quad Fib(n)=Fib(n-1)+Fib(n-2)\ \text{for}\ n\ge 2. $$

To efficiently compute the Fibonacci numbers for potentially large indices, you are encouraged to use matrix exponentiation.

inputFormat

The input consists of a single line containing two space-separated integers a and b (0 ≤ a, b ≤ 10⁶). These represent the indices for which you need to compute the GCD Fibonacci number.

Note: The input is provided via standard input (stdin).

outputFormat

Output a single integer, which is the value of Fib(\gcd(a, b)).

The output should be written to standard output (stdout).

## sample

10 15

5