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 \le b). You want to find the minimum integer l (1 \le l \le b-a+1) such that for any integer x (a \le x \le 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.

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

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