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
        result : Natural := 1;
    begin
        for i in 1 .. n loop
            result := result * i;
        end loop;

        return result;
    end factorial;

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

        while bb > 0 loop
            r := aa mod bb;

            aa := bb;
            bb := r;
        end loop;

        return aa;
    end gcd;

    function gcdExtended(a : Integer; b : Integer; x : out Integer; y : out Integer) return Integer is
        x1 : Integer := 0;
        y1 : Integer := 1;
        q : Integer;
        tempX, tempY, tempB : Integer;
        aa : Integer := a;
        bb : Integer := b;
    begin
        x := 1;
        y := 0;
        while bb /= 0 loop  
            q := aa / bb;
            tempX := x - q * x1;
            tempY := y - q * y1;
            x := x1;
            y := y1;
            x1 := tempX;
            y1 := tempY;
     
            tempB := aa - q * bb;
            aa := bb;
            bb := tempB;
        end loop;

        return aa;
    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;