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 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 x_i and y_i (1 ≤ x_i, y_i ≤ 10⁶). Each of these lines represents a testcase.

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