H. coprime
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

How many positive integer sequences of length $$$n$$$ satisfy that $$$1 \le a_i \le m$$$, and the adjacent elements are coprime.

The answer maybe too large, so you only need to output the result of its modulo of 998244353.

Input

Two positive ingeter $$$n(1\le n \le 1000)$$$,$$$m(1\le m \le 1000)$$$.

Output

An integer represents the answer.

Example
Input
2 5
Output
19