Prime Interval Length

Problem Description

For an interval $[l, r]$ and an integer $k$, it is called a prime interval if and only if the number of primes in that interval is at least $k$.

Given the interval $[l, r]$ and $k$, find the minimum length $len$ such that for every $x \in [l, r - len + 1]$, the interval $[x, x + len - 1]$ is a prime interval.

Input Format

One line with three integers $l, r, k$, as described ($1 \le l \le r \le 10^6$, $0 \le k \le 10^6$).

Output Format

Output one integer $len$ on a single line.

If no such $len$ exists, output $-1$.

Sample Input

6 14 2

Sample Output

6

Constraints

$1 \le l \le r \le 10^6$, $0 \le k \le 10^6$.