CF893E Counting Arrays

You are given two positive integer numbers $ x $ and $ y $ . An array $ F $ is called an $ y $ -factorization of $ x $ iff the following conditions are met: - There are $ y $ elements in $ F $ , and all of them are integer numbers; - . You have to count the number of pairwise distinct arrays that are $ y $ -factorizations of $ x $ . Two arrays $ A $ and $ B $ are considered different iff there exists at least one index $ i $ ( $ 1

The first line contains one integer $ q $ ( $ 1

Print $ q $ integers. $ i $ -th integer has to be equal to the number of $ y_{i} $ -factorizations of $ x_{i} $ modulo $ 10^{9}+7 $ .

In the second testcase of the example there are six $ y $ -factorizations: - $ {-4,-1} $ ; - $ {-2,-2} $ ; - $ {-1,-4} $ ; - $ {1,4} $ ; - $ {2,2} $ ; - $ {4,1} $ .