Counting Arrays

题意翻译

本题是多组数据 对于每组数据，给出x和y，求一个长度为y的序列，其乘积为x，允许有负数，求这种序列的个数，对1e9+7取模。 感谢 @ObsdianGungnir 提供的翻译。

题目描述

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 $ A_{i}≠B_{i} $ . Since the answer can be very large, print it modulo $ 10^{9}+7 $ .

输入输出格式

输入格式

The first line contains one integer $ q $ ( $ 1<=q<=10^{5} $ ) — the number of testcases to solve. Then $ q $ lines follow, each containing two integers $ x_{i} $ and $ y_{i} $ ( $ 1<=x_{i},y_{i}<=10^{6} $ ). Each of these lines represents a testcase.

输出格式

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

输入输出样例

输入样例 #1

2
6 3
4 2

输出样例 #1

36
6

说明

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