C. Primes on Intervaltime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou'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.InputA single line contains three space-separated integers a, b, k (1 ≤ a, b, k ≤ 106; a ≤ b).OutputIn a single line print a single integer — the required minimum l. If there's no solution, print -1.ExamplesInput2 4 2Output3Input6 13 1Output4Input1 4 3Output-1
Input2 4 2
Output3
['binary search', 'number theory', 'two pointers', '*1600']