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A ball of volume V=8 L is full of air with pressure higher than atmospheric pressure by Δp=2×10^4 Pa. The total mass of the ball and the air inside is 200 g. The ball is tossed up to a height h=20 m, then it falls down, collides with the ground, and bounc...

f(x) is a polynomial with integer coefficients and degree at most 10. There are N distinct integer values for which f(n)=2, and M distinct integer values for which f(m)=−2. What is the maximum possible value of NM?