with Ada.Strings; use Ada.Strings;
with Ada.Strings.Unbounded; use  Ada.Strings.Unbounded;

package body Module is

    function factorial(n : Natural) return Natural is
    begin
        if (n = 0 or n = 1 ) then
            return 1;
        end if;

        return n * factorial(n - 1);
    end factorial;

    function gcd(a : Natural; b : Natural) return Natural is
    begin
        if b = 0 then
            return a;
        end if;

        return gcd(b, a mod b);
    end gcd;

    function gcdExtended(a : Integer; b : Integer; x : out Integer; y : out Integer) return Integer is
        x1 : Integer;
        y1 : Integer;
        d : Integer;
    begin
        if b = 0 then
            x := 1;
            y := 0;
            return a;
        end if;
        
        d := gcdExtended(b, a rem b, x1, y1);

        x := y1;
        y := x1 - y1 * (a / b);

        return d;
    end gcdExtended;

    function diophantine(a : Integer; b : Integer; c : Integer) return Result is
        r : Result;
        x0 : Integer := 0;
        y0 : Integer := 0;
        g : Integer := gcdExtended(abs a, abs b, x0, y0);
    begin
        r.n := 0;
        r.m := 0;
        r.resultExists := False;

        if a = 0 and b = 0 then
            return r;
        end if;

        if (c rem g) /= 0 then    
            return r;
        end if;

        x0 := x0 * (c / g);
        y0 := y0 * (c / g);
        if a < 0 then
            x0 := -x0;
        end if;
        if b < 0 then
            y0 := -y0;
        end if;
        r.n := x0;
        r.m := y0;
        r.resultExists := True;

        return r;
    end diophantine;

end Module;