Description

There is a function d(n) which indicates the number of factors for the interger n. You are given two intergers n and m and need to calculate the following formula：

Duing to the large result, so the answer is supposed to modulo 998244353.

Format

Input

The input contains several test cases and the number of test cases is no more than 3000. For each test case contains one line while contains two intergers n and m. $(1 \leq n,m \leq 100000)$

Output

For each test case, output a interger in one line for the value of the answer modulo 998244353.

Samples

10 10

596