Diffie-Hellman and the last bit

Let p=10007p = 10007 and g=5. g=5. You may assume that p p is prime and g g is a primitive root mod p.p.

Suppose Alice and Bob are carrying out the Diffie-Hellman protocol with these parameters. As a first step, Alice sends Bob gm(modp) g^m \pmod p and Bob sends Alice gn(modp), g^n \pmod p, where mm and nn are secret positive integers less than p, p, known only to Alice and Bob, respectively.

An eavesdropper Eve knows the values of p p and g g, and sees the transmissions. In particular, she sees that Alice sends Bob the number 2 2 and Bob sends Alice the number 3. 3. What can Eve deduce about mm and nn quickly? (That is, much more quickly than computing m m and nn--please don't compute mm and nn to solve the problem!)

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