From f4e1f7f58a2f0ff66462ebc8a16d2a0b32dbc7b3 Mon Sep 17 00:00:00 2001
From: aniakubik <ania.kubik@gmail.com>
Date: Fri, 25 Oct 2019 17:42:51 +0200
Subject: [PATCH] extended eucildean algorithm

---
 Math/extendedEuclidian.cpp | 51 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 Math/extendedEuclidian.cpp

diff --git a/Math/extendedEuclidian.cpp b/Math/extendedEuclidian.cpp
new file mode 100644
index 000000000..ad9846a87
--- /dev/null
+++ b/Math/extendedEuclidian.cpp
@@ -0,0 +1,51 @@
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+
+/*
+    for numbers a, b returns x, y such as x * a + y * b = gcd(a,b)
+*/
+
+pair<int,int> extendedEuclidian(int a, int b) {
+	int a_old = a, b_old = b;
+	if(a < b) swap(a,b);
+
+	int x = 0, y = 1, old_x = 1, old_y = 0;
+
+	int quotient, residue;
+	while (b) {
+		quotient = a / b;
+		residue = a % b;
+
+		a = b;
+		b = residue;
+
+		int temp;
+
+		temp = x;
+		x = old_x - quotient * x;
+		old_x = temp;
+		
+
+		temp = y;
+		y = old_y - quotient * y;
+		old_y = temp;
+	}
+
+	if(b_old > a_old) swap(old_x, old_y);
+
+	return make_pair(old_x, old_y); 
+
+}
+
+int main() {
+
+	int a, b;
+	cin >> a >> b;
+	pair<int,int> result = extendedEuclidian(a, b);
+
+	cout<< result.first << " " << result.second;
+
+
+}
\ No newline at end of file