Given two positive integers $n$ and $m$.

You have a positive integer $M$, initially $M=1$. You will perform several operations. In each operation, you choose an integer $x$ uniformly at random from $[1, n]$ and update $M := M \times x$. The process stops when $M > m$.

Calculate the expected number of operations.

It can be proven that the answer is always a rational number. Let it be $\frac{a}{b}$ (where $a$ and $b$ are coprime positive integers, and it is guaranteed that $b$ is not a multiple of $998244353$). You need to output an integer $x$ such that $0 \le x < 998244353$ and $a \equiv bx \pmod{998244353}$. It can be proven that such an $x$ exists and is unique.

Input

A single line containing two positive integers $n$ and $m$.

Output

A single line containing an integer $x$, as defined in the problem description.

Examples

Input 1

3 2

Output 1

748683267

Note 1

The answer is $\frac{9}{4}$, and $4 \times 748683267 \equiv 9 \pmod{998244353}$.

Input 2

2 39

Output 2

12

Input 3

316 12048

Output 3

638683159

Constraints

This problem consists of 10 test cases, each worth 10 points.

For all test cases, $2 \le n \le 9 \times 10^8$ and $1 \le m \le 10^9$.