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(14, 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 14 1 1 0 0 1
1 14 1 1 0 0 1 13 7 2 14 1 7
2 7 1 1 7 0 1 6 0 1 8 1 8 3 2 22 1 11
3 3 1 1 11 0 1 2 0 1 12 1 12 1 2 26 1 13
4 1 1 1 13 0 1 0
5 1 1 1 13 0 1 0
6 1 1 1 13 0 1 0
7 1 1 1 13 0 1 0
(1)(14) - (13)(1) = 1