## Array Product

### Problem Description

You are given a list of N integers and another positive integer K. Write a program to compute the number of ways in which the product P of the given N integers can be expressed as a product of K positive integers (not necessarily distinct). The order of the factors in the expression is not important. For example, 1 x 2 x 3 and 2 x 3 x 1 are not counted as different ways of expressing 6 as a product of three integers.

### Constraints

The product of the N integers <= 10^9

Each of the N integers <=5000

### Input Format

### Output

One line containing the number of ways in which the product of the N integers can be expressed as a product of K positive integers

### Explanation

**Example 1**

Input

2 4

2 3

Output

2

Explanation

The product of the given integers is 6. This can be expressed as a product of 4 integers in 2 ways: 1x1x1x6, 1x1x2x3

**Example 2**

Input

2 3

4 16

Output

7

Explanation

The product is 64. This can be expressed as a product of three integers in the following ways:

1 x 1 x 64

1 x 2 x 32

1 x 4 x 16

1 x 8 x 8

2 x 2 x 16

2 x 4 x 8

4 x 4 x 4