Extended Euclidean algorithm

The objective of the extended Euclidean algorithm is to compute the greatest common denominator of two natural numbers and solve Bézout’s identity

$ax+by=d$.

Given two positive integers a and b, this Diophantine equation is solved for integers x, y, which will not both be positive, and $d=\gcd(a,b)$.

If $d=1$, the algorithm yields the modular multiplicative inverses of a mod b and b mod a since in this case the congruences

$ax\equiv 1\mod b$

and

$by\equiv 1\mod a$

are solved. Here is a naïve C++ implementation of pseudocode found on Wikipedia.

#include <iostream>
#include <cassert>

int main(int argc, char **argv) {
    long int a,b,q,r0,r1,r,s0=1,s1,s=0,t0=0,t1,t=1;
    std::cout << "Enter two integers: ";
    std::cin >> a >> b;
    assert(a > 0 && b > 0); r0=a; r=b;
    while(r>0) {
        q=r0/r;
        r1=r0-q*r; r0=r; r=r1;
        s1=s0-q*s; s0=s; s=s1;
        t1=t0-q*t; t0=t; t=t1;
    }
    std::cout
        << "Bézout coefficients: "
            << s0 << ", " << t0 << std::endl
        << "greatest common divisor: "
            << r0 << std::endl
        << "quotients by the gcd: "
            << t << ", "<< s << std::endl;
    return 0;
}