Let P(x)P(x)P(x) be a polynomial of degree 4 such that P(k)=1kP(k) = \frac{1}{k}P(k)=k1 for k=1,2,3,4,5k = 1, 2, 3, 4, 5k=1,2,3,4,5. What is the value of P(6)P(6)P(6)?
16\frac{1}{6}61
0
1720\frac{1}{720}7201
5144\frac{5}{144}1445