DIVCNTK - Counting Divisors (general)

题意翻译

$\sigma_0(i)$ 表示$i$ 的约数个数 求$S_k(n)=\sum_{i=1}^n\sigma_0(i^k)\mod 2^{64}$ 多测,$T\le10^4,n,k\le10^{10}$ Translated by @Kelin

题目描述

Let $ \sigma_0(n) $ be the number of positive divisors of $ n $ . For example, $ \sigma_0(1) = 1 $ , $ \sigma_0(2) = 2 $ and $ \sigma_0(6) = 4 $ . Let $$ S_k(n) = \sum _{i=1}^n \sigma_0(i^k). $$ Given $ n $ and $ k $ , find $ S_k(n) \bmod 2^{64} $ .

输入输出格式

输入格式


There are multiple test cases. The first line of input contains an integer $ T $ ( $ 1 \le T \le 10000 $ ), indicating the number of test cases. For each test case: The first line contains two integers $ n $ and $ k $ ( $ 1 \le n, k \le 10^{10} $ ).

输出格式


For each test case, output a single line containing $ S_k(n) \bmod 2^{64} $ .

输入输出样例

输入样例 #1

5
1 3
2 3
3 3
10 3
100 3

输出样例 #1

1
5
9
73
2302