E. Counting Arraystime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputPrint q integers. i-th integer has to be equal to the number of yi-factorizations of xi modulo 109 + 7.ExampleInput26 34 2Output366NoteIn the second testcase of the example there are six y-factorizations:  { - 4,  - 1};  { - 2,  - 2};  { - 1,  - 4};  {1, 4};  {2, 2};  {4, 1}. 
Input26 34 2
Output366
['combinatorics', 'dp', 'math', 'number theory', '*2000']