(Extended Euclidean Algorithm)

Today, I roughly learned the Extended Euclidean algorithm.

Set A, B, and C as any integer, and G = gcd (A, B). The solution of the equation AX + by = G is (x1, Y1 ), when C is a multiple of G, a group of solutions for AX + by = C is (x1 * C/g, Y1 * C/G ); if C is not a multiple of G, there is no integer solution.

Ultraviolet A 10104:

He Problem

From Euclid it is known that for any positive integersAAndBThere exist such IntegersXAndYThatAx + by = d, WhereDIs the greatest common divisorAAndB.
The problem is to find for givenAAndBCorrespondingX,YAndD.

The input

The input will consist of a set of lines with the integer numbersAAndB, Separated with space (A, B <1000000001).

The output

For each input line the output line shoshould consist of three IntegersX, YAndD,Separated with space. If there are several suchXAndY, You shoshould output that pair for which| X | + | Y |Is
The minimal (primarily) andX <= y(Secondarily ).

Sample Input

4 617 17

Sample output

-1 1 20 1 17

Code:

# Include <cstdio>
Void gcd (int A, int B, Int & D, Int & X, Int & Y)
{
If (B = 0)
{
D =;
X = 1; y = 0;
}
Else
{
Gcd (B, A % B, D, Y, X );
Y-= x * (A/B );
}
}
Using namespace STD;
Int main ()
{

Int A, B, D, X, Y;
While (scanf ("% d", & A, & B )! = EOF)
{
Gcd (A, B, D, x, y );
Printf ("% d \ n", X, Y, d );
}
Return 0;
}