Consider the following variant on Diffie$-$Hellman:

$(1)$ Alice and Bob publicly agree on a prime $p$ and a generator $g$ for $Z_p.$ All

computations are done modp.

$(2)$ Alice and Bob each decide on their private keys $x_A,x_B,$ and compute and

make public their public keys $g^{x_A},g^{x_B}$

$(3)$ When Alice and Bob communicate: Alice generates $r_A$ at random, and

sends $g^{r_A}$ to Bob. Bob generates $r_B$ at random, and sends $g^{r_B}$ to Alice.

$(4)$ The shared key for the session is $g^{r_A{x}_B+r_B{x}_A}.$ Alice computes this as

$(g^{r_B}{)}^{x_A}(g^{x_B}{)}^{r_A},$ and Bob computes this as $(g^{x_A}{)}^{r_B}(g^{r_A}{)}^{x_B}.$

Suppose $p=79$ and $g=3,$ Alice's public key is $64$ and Bob's public key is $57.$

Suppose Alice and Bob start a communication session with $g^{r_A}=28$ and $g^{r_B}=$

Find the shared key for the session.