IMO 1969 LL CZS15

Let K1, . . . , Kn be nonnegative integers. Prove that

IMO 1969 LL CZS15

Origin: CZS

Problem

Let K1, . . . , Kn be nonnegative integers. Prove that K1!K2! \cdot \cdot \cdot Kn! \geq[K/n]!n, where K = K1 + \cdot \cdot \cdot + Kn.