Given an array ~A~ of ~N~ prime numbers: ~A_1, A_2, ..., A_N~, a beautiful number is a number that is divisible by at least one prime number in the array ~A~.

Task: Given the integer ~N~ and the array ~A~, count the number of beautiful numbers that do not exceed ~M~.

Input:

• The first line contains two integers ~N~ and ~M~ (~1 ≤ N ≤ 20~);
• The second line contains the sequence of integers ~A_1, A_2, ..., A_N~. The numbers are separated by spaces.

Output:

• A single integer representing the number of beautiful numbers.

Sample Input

2 11  
3 5

Sample Output

5

Notes

• The beautiful numbers are: ~3, 5, 6, 9, 10~.

Constraints

• ~60\%~ of the test cases correspond to ~1 ≤ M ≤ 10^6~, ~1 ≤ A_i ≤ 10^5~;
• ~20\%~ of the test cases correspond to ~1 ≤ M ≤ 10^9~, ~10^5 < A_i ≤ 10^9~;
• ~20\%~ of the test cases correspond to ~1 ≤ M ≤ 10^{18}~, ~1 ≤ A_i ≤ 10^{18}~.