# Array Product

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