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# Why ElGamal signature is insecure with nonrandom k?

In ElGamal signature scheme like:

keygen: $$\beta=\alpha^a\ (mod\ p)$$ where $$\alpha$$ and $$p$$ are large prime numbers. public key is $$(p,\alpha,\beta)$$ and secret key is $$a$$.

Sign: Choosing random $$k$$ that $$gcd(k,p-1)=1$$, calucalting $$r:=a^k\ (mod\ p)$$ and $$s:=k^{-1}.(m-ar)\ (mod\ p-1)$$ then we send $$(m,r,s)$$

Verify: calculating $$v_1:=\beta^r.r^s (mod\ p)$$ and $$v_2:= \alpha^m (mod\ p)$$ if $$v_1$$ and $$v_2$$ be equal we verify this sign.

In the booklet, I'm reading for cryptography course said if $$k$$ be non-random this signature scheme is insecure. what's the reason?