## Editorial for Isolation Game

Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.

Submitting an official solution before solving the problem yourself is a bannable offence.

Editorialist: PHPeasant

Isolation Game is the first problem in the Unigames section of the 2020 Charity Unvigil Contest where you need to determine the winner in a very simple game. The sneaky trick is that a player the depletes the stack to 0 also looses.

The intended solution is to implement the game using Euclid's GCD algorithm. A verbose but explicit example implementation in C++ 14 is given below:

#include <bits/stdc++.h>
using namespace std;

int gcd(int a , int b){
int t;
while(b!=0){
t = b;
b = a % b;
a = t;
}
return a;
}

int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int a,b,n, curr;
cin >> a >> b >> n;
int winner = 0;
while(true){
//Taylor move
curr = gcd(b, n);
if(curr<n){
n-=curr;
winner = 1;
} else {
winner = 0;
break;
}
if(n == 0){
winner = 1;
break;
}
//Gozz's move
curr = gcd(a, n);
if(curr < n){
n-=curr;
winner = 0;
} else {
winner = 1;
break;
}
if(n == 0){
winner = 0;
break;
}
}
cout << winner;
return 0;
}