Binary Trees With Factors
Given an array of unique integers, arr, where each integer arr[i] is strictly greater than 1.
We make a binary tree using these integers, and each number may be used for any number of times. Each non-leaf node's value should be equal to the product of the values of its children.
Return the number of binary trees we can make. The answer may be too large, so return the answer modulo 10^9 + 7.
Example 1
Input
arr = [2,4]Output
3We can make these trees:
[2], [4], and [4, 2, 2].Example 2
Input
arr = [2,4,5,10]Output
7We can make these trees:
[2], [4], [5], [10], [4, 2, 2], [10, 2, 5], and [10, 5, 2].Constraints
- 1 <= arr.length <= 1000
- 2 <= arr[i] <= 10^9
- All the values of arr are unique.
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