A8687 | Primes on Interval

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.

A single line contains three space-separated integers $a,b,k$ ( $1<=a,b,k<=10^{6}; a<=b$ ).

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