Kitani likes finding beauty in mathematics, especially in number theory. During the search, the following interesting equation was found:

where U and M — are given positive integers.

Here, φ(n) — is Euler’s totient function: the number of integers from 1 to n that are coprime with n, that is, their greatest common divisor with n is 1. For example, φ(10) = 4 — these numbers are 1, 3, 7, 9.

ω(n) — is the number of different prime divisors of n. For example, ω(60) = 3 — these numbers are 2, 3, 5.

Now Kitani is interested in how many solutions in positive integers this equation has. After a long search, there is almost no time left, so now this task is passed to you.

The only line contains integers U and M (1 ≤ U, M ≤ 10⁵).

Print one integer — the number of solutions of the equation in positive integers.

The solution in the first example:

• φ(1) + 1 · ω(1 · 1) = 1 + 1 · 0 = 1

The solutions in the second example:

• φ(30) + 19 · ω(19 · 30) = 8 + 19 · 4 = 84
• φ(47) + 19 · ω(19 · 47) = 46 + 19 · 2 = 84