X = 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15
Y = 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15
X ↔ Y

Ext-GCD(12, 1) :

i GCD Bezout AOdd : AEven :
A B ax ay bx by |A-B| A↔B Sx Sy ax
Sx'
ay
Sy'
A
A/2
ax
ax + Y
ay
ay + X
ax
ax/2
ay
ay/2
0 12 1 1 0 0 1
1 12 1 1 0 0 1 11 6 2 12 1 6
2 6 1 1 6 0 1 5 3 2 18 1 9
3 3 1 1 9 0 1 2 0 1 10 1 10 1 2 22 1 11
4 1 1 1 11 0 1 0
5 1 1 1 11 0 1 0
6 1 1 1 11 0 1 0
7 1 1 1 11 0 1 0
(1)(12) - (11)(1) = 1