Problem Statement

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

Input

Input is given from Standard Input in the following format:
N K

Output

Print the answer.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分