Problem Description

Given $n, m$, with $m \le n$ guaranteed, define $F(a,b)=\sum_{i=0}^{b}\binom{b}{i}\binom{n-i}{a}$.

Find $\bigoplus_{a=1}^{m}\bigoplus_{b=1}^{m}(F(a,b) \bmod 998244353)$.

Here $\oplus$ denotes the XOR operation.

Input Format

The first line contains two integers $n, m$, with the same meaning as in the statement.

Output Format

Output one integer representing the answer.

3 3

7

Hint

【Constraints】

This problem uses bundled testdata.

For $100\%$ of the testdata, $1 \le n \le {10}^9$, $1 \le m \le 5000$, and $m \le n$ is guaranteed.

• Subtask 1 (20 points): $n \le 500$.
• Subtask 2 (30 points): $n \le 5000$.
• Subtask 3 (50 points): no special constraints.

Translated by ChatGPT 5