## Goal

Starting at coordinates (0,0) with D[0]=0, a random direction generator D[n+1] = (a*D[n]+b) mod m tells you which direction to go next (where D mod 4=0,1,2,3 indicates Up, Down, Left, Right). How many steps does it take to get back to (0,0)?
Input

**Line 1:** `a`

**Line 2:** `b`

**Line 3:** `m`

Output

The number of steps.

Constraints

1≤ `a`,`b`,`m` ≤ 100,000

steps ≤ 500,000