Counting Arrays

3000ms

262144K

Description:

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;
$\text{[math]}$ .

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 A_i ≠ B_i. Since the answer can be very large, print it modulo 10⁹ + 7.

Input:

The first line contains one integer q (1 ≤ q ≤ 10⁵) — the number of testcases to solve.

Then q lines follow, each containing two integers x_i and y_i (1 ≤ x_i, y_i ≤ 10⁶). Each of these lines represents a testcase.

Output:

Print q integers. i-th integer has to be equal to the number of y_i-factorizations of x_i modulo 10⁹ + 7.

Sample Input:

2
6 3
4 2

Sample Output:

36
6

Note:

In the second testcase of the example there are six y-factorizations:

{ - 4, - 1};
{ - 2, - 2};
{ - 1, - 4};
{1, 4};
{2, 2};
{4, 1}.

Informação

Provedor Codeforces

Código CF893E