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B - Product of Divisors /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

A^{B} の正の約数の総積は A で最大何回割り切れますか。

### 制約

• 2\leq A\leq 10^{12}
• 0\leq B\leq 10^{18}
• 入力は全て整数

### 入力

A B


### 入力例 1

2 3


### 出力例 1

6


A^{B}=8 の正の約数は 1,2,4,8 で、その総積は 64 となります。 6426 回割り切れるので、6 を出力します。

### 入力例 2

924 167


### 出力例 2

867046524


### 入力例 3

167167167167 0


### 出力例 3

0


Score : 500 points

### Problem Statement

At most how many times can the product of all positive divisors of A^{B} be divided by A?

It can be shown from the constraints that this count is finite, so find it modulo 998244353.

### Constraints

• 2\leq A\leq 10^{12}
• 0\leq B\leq 10^{18}
• All input values are integers.

### Input

The input is given from Standard Input in the following format:

A B


### Sample Input 1

2 3


### Sample Output 1

6


The positive divisors of A^{B}=8 are 1, 2, 4, and 8, whose product is 64. 64 can be divided by 2 at most six times, so print 6.

### Sample Input 2

924 167


### Sample Output 2

867046524


### Sample Input 3

167167167167 0


### Sample Output 3

0