Score : $600$ points

问题陈述

求一个二项式系数 $\displaystyle \binom{N}{K}$ 的正除数的数量，模 $998244353$。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Find the number, modulo $998244353$, of positive divisors of a binomial coefficient $\displaystyle \binom{N}{K}$.

Constraints

• $1 \leq N \leq 10^{12}$
• $0 \leq K \leq \min(10^6,N)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$

Output

Print the answer.

Sample Input 1

5 2

Sample Output 1

4

We have $\displaystyle \binom{5}{2}=10$, which has four positive divisors: $1,2,5,10$.

Sample Input 2

103 3

Sample Output 2

8

We have $\displaystyle \binom{103}{3}=176851$, which has eight positive divisors.

Sample Input 3

1000000000000 1000000

Sample Output 3

110520107

update @ 2024/3/10 09:57:36