Factors of a Number

题号：NC218169
时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

Define a function d(n), representing the quantity of factors of a positive integer a.

For example, the expression d(12) = 6 representing the number 12 have 6 factors - 1, 2, 3, 4, 6, 12.

Given l, r and k, determine the value of

$\sum_{i=l}^{r}d(i^{k}) \mod\ 998244353$

Three integers l, r and k, separated by space.

The value of the expression.

示例1

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1 5 1

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示例2

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1 10 2

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示例3

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1 100 3

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1 <= l, r, k <= 1000