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, 14) → Twos = 1 → Ext-GCD(6, 7) :

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 6 7 1 0 0 1
1 6 7 1 0 0 1 1 3 8 6 4 3
2 3 7 4 3 0 1 4 1 4 4 4 4 2 Even Even 2 2
3 2 3 2 2 4 3 1 1 Even Even 1 1
4 1 3 1 1 4 3 2 1 5 4 5 4 1 12 10 6 5
5 1 1 6 5 1 1 0
6 1 1 6 5 1 1 0
7 1 1 6 5 1 1 0
(6)(12) - (5)(14) = 2