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G - Divisors of Binomial Coefficient /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 制約

• 1 \leq N \leq 10^{12}
• 0 \leq K \leq \min(10^6,N)
• 入力に含まれる値は全て整数である

### 入力

N K


### 入力例 1

5 2


### 出力例 1

4


\displaystyle \binom{5}{2}=10 です。10 の正の約数は 1,2,5,104 個です。

### 入力例 2

103 3


### 出力例 2

8


\displaystyle \binom{103}{3}=176851 です。176851 の正の約数は 8 個あります。

### 入力例 3

1000000000000 1000000


### 出力例 3

110520107


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


### 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