Gauss 5a

#include <cstddef>
#include <cassert>
#include <iostream>

using namespace std;

const size_t N = 4;

long long A[N][N + 1] = {
    {-7, 4, -14, 18, 0},
    {9, -5, 18, -23, -3},
    {-2, 2, -4, 6, -9},
    {-8, -7, -16, 9, 0}
};

long long gcd(long long a, long long b) {
    while (b) {
        a %= b;
        swap(a, b);
    }
    return a;
}

void solve(size_t I, size_t J) {
    if (I == N) return;
    size_t L = -1;
    for (size_t i = I; i < N; ++i)
        if (L == -1 && A[i][J]) L = i;
    if (L == -1) return;
    for (size_t i = I; i < N; ++i) {
        if (i == L || !A[i][J]) continue;
        long long k1 = A[L][J];
        long long k2 = A[i][J];
        long long g = gcd(k1, k2);
        k1 /= g;
        k2 /= g;
        for (size_t j = J; j <= N; ++j) {
            A[i][j] *= k1;
            A[i][j] -= k2 * A[L][j];
        }
    }
    solve(I + 1, J + 1);
}

int main() {
    solve(0, 0);
    for (size_t i = 0; i < N; ++i) {
        for (size_t j = 0; j <= N; ++j)
            printf("%lld ", A[i][j]);
        printf("\n");
    }
}