Let Px be a polynomial whose coefficient are integers satisfying P(1) = 5,  P (2) = 7. Then smallest possible positive value of P(10) is of the form ab then a + b = _____

Let P(x)=q(x)(x−1)(x−2)+lx+m       since P1=5⇒l+m=5                P2=7⇒2l+m=7             ⇒l=2 and m=3P(x)=q(x)(x−1)(x−2)+2x+3P(10)=q(10)⋅(72)+23 Least value of P10=23 where  q(10)=0