Floor Function Power!

k=0mn1exp1(km+kn) \large \sum_{k=0}^{mn-1} \exp_{-1} \Bigg ( \left \lfloor \frac km \right \rfloor + \left \lfloor \frac kn \right \rfloor \Bigg)

Let mm and nn be relatively prime positive integers such that mnmn is odd. Then what is the value of summation above.

Note the notation, expAB=AB\exp_A B = A^B .

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