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(2, 13) :

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 2 13 1 0 0 1
1 2 13 1 0 0 1 11 1 14 2 7 1
2 1 13 7 1 0 1 12 1 7 2 7 2 6 20 4 10 2
3 6 1 10 2 7 1 5 3 Even Even 5 1
4 3 1 5 1 7 1 2 0 12 2 12 2 1 Even Even 6 1
5 1 1 6 1 7 1 0
6 1 1 6 1 7 1 0
7 1 1 7 1 6 1 0
(7)(2) - (1)(13) = 1