Algorithm
B. Weird Subtraction Process
time limit per test
1 secondmemory limit per test
256 megabytesproblem link- https://codeforces.com/contest/946/problem/B
input
standard inputoutput
standard outputYou 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.
Examples
input
Copy
12 5
output
Copy
0 1
input
Copy
31 12
output
Copy
7 12
Note
Explanations to the samples:
- a = 12, b = 5
a = 2, b = 5 a = 2, b = 1 a = 0, b = 1; - a = 31, b = 12 a = 7, b = 12.
Code Examples
#1 Code Example with C++ Programming
Code -
C++ Programming
#include <bits/stdc++.h>
using namespace std;
int main() {
long long a, b;
cin >> a >> b;
bool ok1 = true, ok2 = true;
while(a != 0 && b != 0 && (ok1 || ok2)) {
ok1 = ok2 = false;
if(a <= 2 * b && a - 2 * b <= 0) {
ok1 = true;
a -= (a / (2 * b)) * 2 * b;
continue;
}
if(b<= 2 * a && b - 2 * a <= 0) {
ok2 = true;
b -= (b / (2 * a)) * 2 * a;
continue;
}
}
cout << a << ' ' << b << endl;
return 0;
}Input
12 5
Output
0 1
Demonstration
Codeforces Solution-Weird Subtraction Process-Solution in C, C++, Java, Python