P7481 Dream Moment

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.

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

Output one integer representing the answer.

**【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