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(0, 8) → Twos = 3 → Ext-GCD(0, 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 0 1 1 0 0 1
1 0 1 1 0 0 1 1
2 0 1 1 0 0 1 1
3 0 1 1 0 0 1 1
4 0 1 1 0 0 1 1
5 0 1 1 0 0 1 1
6 0 1 1 0 0 1 1
7 1 0 0 1 1 0 1
GCD = 1; P, Q Prohibited (X = 0, so Q is negative)