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Unit Power Subsets
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Unit Power Subsets

Contributed by
TanishkTonk
Hard
yellow-spark
0/120
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Problem Statement

You are given an integer array ‘Arr’. You are required to calculate the number of subsets whose product can be represented as the product of unit powers of one or more distinct primes. As the answer can be large calculate it modulo (10^9+7).

Note: Subsets are considered distinct if the chosen set of indexes are different.
For Example:
Suppose arr = [1, 3, 9, 5]

Valid subsets are as follows:
[3], Product = 3.
[1, 3], Product = 1 * 3.
[5], Product = 5.
[1, 5], Product = 1 * 5.
[3, 5], Product = 3 * 5.
[1, 3, 5], Product = 1 * 3 * 5.
All of the above subsets’ products can be represented only with unit powers of prime and have at least one prime in their product. Hence they are valid. As we have six valid subsets, our output will be 6.
Detailed explanation ( Input/output format, Notes, Constraints, Images )
Sample Input 1 :
2
4
1 3 9 5
3
14 15 2
Sample Output 1 :
6
5
Explanation For Sample Input 1 :
For First Case - Same as explained in above example.

For the second case - 

arr = [14, 15, 2]
[14], Product = 2 * 7.
[15], Product = 3 * 5.
[2], Product = 2.
[14, 15], Product = 2 * 3 * 5 * 7.
[2, 15], Product = 2 * 3 * 5.
All of the above subsets’ products can be represented only with unit powers of prime and have at least one prime in their product. Hence they are valid. As we have five valid subsets, our output will be 6.
Sample Input 2 :
2
7
1 2 3 4 5 6 7
8
1 5 2 8 1 7 1 9
Sample Output 2 :
38
56
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