102276: [AtCoder]ABC227 G - Divisors of Binomial Coefficient

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

问题描述

求二项式系数$\displaystyle \binom{N}{K}$的正约数个数，对$998244353$取模。

限制条件

• $1 \leq N \leq 10^{12}$
• $0 \leq K \leq \min(10^6,N)$
• 输入中的所有值都是整数。

输入

从标准输入以以下格式获取输入：

$N$ $K$

输出

打印答案。

样例输入1

5 2

样例输出1

4

我们有$\displaystyle \binom{5}{2}=10$，它有四个正约数：$1,2,5,10$。

样例输入2

103 3

样例输出2

8

我们有$\displaystyle \binom{103}{3}=176851$，它有八个正约数。

样例输入3

1000000000000 1000000

样例输出3

110520107