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  1. Prepare
  2. Mathematics
  3. Number Theory
  4. Unfriendly Numbers

Unfriendly Numbers

Given friendly number and unfriendly numbers, determine how many numbers are divisors of the friendly number but not the unfriendly numbers.

Input Format

The first line contains space-separated integers, (the number of unfriendly numbers) and (the friendly number), respectively. The second line contains space-separated unfriendly numbers.

Constraints

Output Format

Print the the number of unique divisors of (i.e.: divisors that are not shared with those of the unfriendly numbers) as a single integer.

Sample Input

8 16
2 5 7 4 3 8 3 18

Sample Output

1

Explanation

There are unfriendly numbers: .
Our friendly number, , is , and its even divisors are .

Let be the number of friendly divisors that are not also unfriendly divisors. Let's determine which divisors of are not also divisors of the unfriendly numbers:

  • is a divisor of all unfriendly numbers, so we disregard it.
  • is a divisor of unfriendly numbers , , and , so we disregard it.
  • is a divisor of unfriendly numbers and , so we disregard it.
  • is a divisor of unfriendly number , so we disregard it.
  • is not a divisor of any unfriendly number, so we increment to .

As there are no more friendly divisors to check, we print the value of (which is ) on a new line.