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G - Divisors of Binomial Coefficient

Score : $600$ points

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.

5 2

4

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

103 3

8

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

1000000000000 1000000

110520107