Task

Let's call two integers A and B friends if each integer from the array divisors is either a divisor of both A and B or neither A nor B. If two integers are friends, they are said to be in the same clan. How many clans are the integers from 1 to k, inclusive, broken into?

Example

For divisors = [2, 3] and k = 6, the output should be 4

The numbers 1 and 5 are friends and form a clan, 2 and 4 are friends and form a clan, and 3 and 6 do not have friends and each is a clan by itself. So the numbers 1 through 6 are broken into 4 clans.

Input/Output

• [input] integer array divisors

  A non-empty array of positive integers.

  Constraints: 2 ≤ divisors.length < 10, 1 ≤ divisors[i] ≤ 10.

• [input] integer k

  A positive integer.

  Constraints: 5 ≤ k ≤ 50.

• [output] an integer