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