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

Input

2 4 2

Output

3

Example 2

Input

2 4 3

Output

-1

Example 3

Input

6 13 1

Output

4