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.

Input

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

Output

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