Clash of the coordinates!

Geometry Level 5

A right triangle has to be constructed with the legs parallel to the axes of co-ordinates. If the equations of the medians to the two legs are \(3x-y+1=0\) and \(mx-y+2=0\), the number of values of \(m\) for which, such a triangle exists can be expressed as a positive integer \(p\). Enter the value of \(p\) as your answer.

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