# Signature scheme doesnt seem to hold

I can't seem to verify this signature scheme.

Taking this as an example: $p = 23$, $g = 7$, Private Key : $(12$, $20$, $3$, $18)$, $y = 16$ and $q = 2$

This will give me:

$y_1 = 7$12$*16$20 $= 13 (mod23)$

$y_2 = 7$3$*16$18 $= 10 (mod23)$

Now signing a message $m = 13$:

$output1 = 12(13) + 3 = 1 (mod 2)$

$output2 = 20(13) + 18 = 0 (mod 2)$

Verifying gives me: