#### Extended Euclid Algorithm

/**
* @file
* @brief GCD using [extended Euclid's algorithm]
* (https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm)
*
* Finding coefficients of a and b ie x and y in  Bézout's identity
* \f[\text{gcd}(a, b) = a \times x + b \times y \f]
* This is also used in finding Modular
* multiplicative inverse of a number. (A * B)%M == 1 Here B is the MMI of A for
* given M, so extendedEuclid (A, M) gives B.
*/
#include <algorithm>  // for swap function
#include <iostream>

/**
* function to update the coefficients per iteration
* \f[r_0,\,r = r,\, r_0 - \text{quotient}\times r\f]
*
* @param[in,out] r signed or unsigned
* @param[in,out] r0 signed or unsigned
* @param[in] quotient  unsigned
*/
template <typename T, typename T2>
inline void update_step(T *r, T *r0, const T2 quotient) {
T temp = *r;
*r = *r0 - (quotient * temp);
*r0 = temp;
}

/**
* Implementation using iterative algorithm from
* [Wikipedia](https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Pseudocode)
*
* @param[in] A unsigned
* @param[in] B unsigned
* @param[out] GCD unsigned
* @param[out] x signed
* @param[out] y signed
*/
template <typename T1, typename T2>
void extendedEuclid_1(T1 A, T1 B, T1 *GCD, T2 *x, T2 *y) {
if (B > A)
std::swap(A, B);  // Ensure that A >= B

T2 s = 0, s0 = 1;
T2 t = 1, t0 = 0;
T1 r = B, r0 = A;

while (r != 0) {
T1 quotient = r0 / r;
update_step(&r, &r0, quotient);
update_step(&s, &s0, quotient);
update_step(&t, &t0, quotient);
}
*GCD = r0;
*x = s0;
*y = t0;
}

/**
* Implementation using recursive algorithm
*
* @param[in] A unsigned
* @param[in] B unsigned
* @param[out] GCD unsigned
* @param[in,out] x signed
* @param[in,out] y signed
*/
template <typename T, typename T2>
void extendedEuclid(T A, T B, T *GCD, T2 *x, T2 *y) {
if (B > A)
std::swap(A, B);  // Ensure that A >= B

if (B == 0) {
*GCD = A;
*x = 1;
*y = 0;
} else {
extendedEuclid(B, A % B, GCD, x, y);
T2 temp = *x;
*x = *y;
*y = temp - (A / B) * (*y);
}
}

/// Main function
int main() {
uint32_t a, b, gcd;
int32_t x, y;
std::cin >> a >> b;
extendedEuclid(a, b, &gcd, &x, &y);
std::cout << gcd << " " << x << " " << y << std::endl;
extendedEuclid_1(a, b, &gcd, &x, &y);
std::cout << gcd << " " << x << " " << y << std::endl;
return 0;
}