E. Counting Arrays
combinatorics; dp; math; number theory
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 ≤ i ≤ y) such that Ai ≠ Bi. Since the answer can be very large, print it modulo 109 + 7.
The first line contains one integer q (1 ≤ q ≤ 105) — the number of testcases to solve.Then q lines follow, each containing two integers xi and yi (1 ≤ xi, yi ≤ 106). Each of these lines represents a testcase.
Print q integers. i-th integer has to be equal to the number of yi-factorizations of xi modulo 109 + 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}.