Prime Protocol

In the kingdom of MAPS, the royal archives contain a sequence of scrolls numbered from $X$ to $Y$. The Prime Minister (literally a minister obsessed with prime numbers) has devised a new Prime Security Protocol to ensure the archives remain safe from spies.

The protocol states that for every window of exactly $M$ consecutive scrolls, there must be at least $K$ prime-numbered scrolls to ensure numerical purity. If a spy tries to extract knowledge from the archives, they will always encounter a sufficient number of prime scrolls in any section, dismantling their evil plans.

As the kingdom's Chief Mathematician, you must determine the smallest possible $M$ that satisfies this protocol. If there exists no valid $M$, report $-1$ to the Prime Minister.

Input

A single line containing three integers $X$, $Y$, $K$.

Output

A single line containing one integer $M$ (if it exists) or $-1$.

Constraints

• $1 \leq X, Y, K, \leq 10^6$
• $X \leq Y$

Example 1

2 4 2

3

Example 2

2 4 3

-1

Example 3

6 13 1

4