P8576 "DTOI-2" Realm of Stars

>Celestials open the blue heavens, and the silver realm loses the dusk.

The stars in the night sky form a sequence $a$. The $i$-th number in the sequence represents the brightness of the $i$-th star. Now, as the favored one of the stars, you have two ways to operate on the stars. - Operation 1: The input format is $\texttt{1 l r x y}$, which means changing the brightness of all stars in $[l,r]$ whose brightness is $x$ to $y$. - Operation 2: The input format is $\texttt{2 l r}$, which means outputting the value of $ \prod\limits_{i = l}^{r} C_{\sum_{j = l}^{i}a_j}^{a_i}\ \bmod 998244353 $.

The first line contains two integers $n,q$, representing the length of the sequence and the number of operations. The second line contains $n$ integers, representing the initial values of the sequence. The next $q$ lines each contain one operation, with the format given above.

For each operation of type $2$, output the required value.

**Sample Explanation #1** It can be obtained by directly computing according to the statement. | $\textbf{Subtask}$ | $n \le$ | $q \le$ | Special Property | Total Score | | :----------: | :---------------: | :---------------: | :-------------: | :---: | | $1$ | $10$ | $15$ | None | $5$ | | $2$ | $10^3$ | $10^3$ | None | $10$ | | $3$ | $5\times 10^4$ | $5\times 10^4$ | Only operation $2$ | $10$ | | $4$ | $5\times 10^4$ | $5\times 10^4$ | Only one operation $2$ | $10$ | | $5$ | $5\times 10^4$ | $5\times 10^4$ | None | $21$ | | $6$ | $10^5$ | $10^5$ | $\sum a[i] \le 5\times 10^5$ | $14$ | | $7$ | $10^5$ | $10^5$ | None | $30$ | For $100\%$ of the testdata, $1 \le n,q,a_i \le 10^5$. Also, $1 \le l,r\le n;1 \le x,y\le 10^5$. At any time, $\sum a$ will not exceed $10^7$. Translated by ChatGPT 5