How to find $r$ for El-Gamal signature with known private key For public key $(g,b,P)$ and private key $x$ I have that...

x = 8437809068483222013573558289468531414326215630180218801941732905
P = 7339893940555892950021117953932742794751344995120378281984000000000001
g = 89
b = 4912876245630500045238873065831524614701581692824065606616840403034906


I am trying to find the random number r used in signing 

M = 178197212211208201211210146110


where the (y,s) are

y = 4888362675268704701803932900979085359299230032137217762234865463825395
s = 2972754454246783222682468852246694620839545754907463463768712881658815


I am using the signature scheme here and I thought I could solve for $r=\frac{M-xy}{s} \mod (P-1)$ but I keep getting 

r=6586066995309612052451381515420731372587693346972879972770753040391021


but then  $y=g^r \mod P$ isn't true.



The instructions indicate:
$r\cdot s\bmod (P-1) = 6586066995309612052451381515420731372587693346972879972770753040391021\cdot 2972754454246783222682468852246694620839545754907463463768712881658815 \bmod 7339893940555892950021117953932742794751344995120378281984000000000000$

yields 

720487199053255869302957380434219754352470619914582568375746711500115,

whereas

$M-x\cdot y\bmod (P-1) = 178197212211208201211210146110-8437809068483222013573558289468531414326215630180218801941732905\cdot 4888362675268704701803932900979085359299230032137217762234865463825395 \bmod 7339893940555892950021117953932742794751344995120378281984000000000000$

yields

4218349912365743958467337126869664026873136130922995548817354564023635.

Are you sure that you invert $s$ modulo $(P-1)$ correctly?

PS: No need to ask a new question for the same problem if you don't get an answer within 6 hours. Most regular users don't look just at the front page. After few days you can then change the text a little bit (like the others do) to get your question to the front page again.