// Contoh Bab 15: algoritma Euclid diperluas.
//
// Mencari x dan y yang memenuhi a*x + b*y = FPB(a, b).
//
// Compile:  g++ -std=c++17 -O2 -o euclidluas exercises/15/03-euclid-luas.cpp
// Jalankan: ./euclidluas
// Contoh masukan: 240 46

#include <iostream>
using namespace std;

long long fpb_luas(long long a, long long b, long long &x, long long &y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    long long x1, y1;
    long long g = fpb_luas(b, a % b, x1, y1);
    x = y1;
    y = x1 - (a / b) * y1;
    return g;
}

int main() {
    long long a, b, x, y;
    cin >> a >> b;

    long long g = fpb_luas(a, b, x, y);

    cout << "FPB = " << g << "\n";
    cout << "x = " << x << ", y = " << y << "\n";
    cout << "periksa: " << a << "*" << x << " + " << b << "*" << y
         << " = " << a * x + b * y << "\n";
    return 0;
}