You've decided to carry out a survey in the theory of prime numbers. Let us remind you that a prime number is a positive integer that has exactly two distinct positive integer divisors. Consider positive integers a , a + 1, ..., b (a ≤ b). You want to find the minimum integer l (1 ≤ l ≤ b - a + 1) such that for any integer x (a ≤ x ≤ b - l + 1) among l integers x , x + 1, ..., x + l - 1 there are at least k prime numbers. Find and print the required minimum l . If no value l meets the described limitations, print -1.

输入描述:

A single line contains three space-separated integers a, b, k (1 ≤ a, b, k ≤ 106; a ≤ b).

输出描述:

In a single line print a single integer — the required minimum l. If there's no solution, print -1.