You have two variables a and b. Consider the following sequence of actions performed with these variables:

If a = 0 or b = 0, end the process. Otherwise, go to step 2;
If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.

Initially the values of a and b are positive integers, and so the process will be finite.

You have to determine the values of a and b after the process ends.

Input

The only line of the input contains two integers n and m (1 ≤ n, m ≤ 10¹⁸). n is the initial value of variable a, and m is the initial value of variable b.

Output

Print two integers — the values of a and b after the end of the process.

Note

Explanations to the samples:

a = 12, b = 5 $\text{[math]}$ a = 2, b = 5 $\text{[math]}$ a = 2, b = 1 $\text{[math]}$ a = 0, b = 1;
a = 31, b = 12 $\text{[math]}$ a = 7, b = 12.

Weird Subtraction Process

Examples