Sequence Construction with Given Product and LCM

Given two integers \(n\) and \(k\), count the number of sequences \([a_1,a_2,\dots,a_k]\) that satisfy the following conditions:

• \(a_1 \times a_2 \times \dots \times a_k = n\).
• \(1 < a_1 \le a_2 \le \dots \le a_k\).
• The least common multiple (\(\mathrm{lcm}\)) of the \(k\) numbers is equal to \(n\), i.e. \(\mathrm{lcm}(a_1,a_2,\dots,a_k)=n\).

Find the number of such sequences.

inputFormat

The input consists of a single line containing two integers \(n\) and \(k\) separated by a space.

Constraints (for example):

• \(2 \le n \le 10^6\)
• \(1 \le k \le 10\)

outputFormat

Output a single integer representing the number of sequences satisfying the conditions.

sample

12 3

0