P7511 Three to Six

“I heard JOJO 6 is coming!” “A great era is coming!” “But that invincible man...” “Ah... before I get stabbed, let me relive ‘Ora Ora’ one more time...”

Given integers $n, k$ and an $n$-th permutation $\pi'$, ask how many permutations $\pi$ satisfy that there are exactly $k$ positions $i$ such that $1 \le i \le n$ and $\pi_i < \pi_{\pi'_i}$. Output the answer modulo $998244353$.

The first line contains two integers $n, k$. The second line contains $n$ positive integers, representing $\pi'$.

Output one line containing one non-negative integer, representing the number of permutations $\pi$ that satisfy the condition.

**Sample Explanation** For the first sample, $\pi_i$ cannot be less than $\pi_i$, so the condition must always be satisfied. Therefore, the answer is $5! = 120$. For the second sample, there are the following $5$ permutations $\pi$ that satisfy the condition: 1. $12345$； 1. $23451$； 1. $34512$； 1. $45123$； 1. $51234$。 For the third sample, no explanation is provided. **Constraints** For $20\%$ of the testdata, $n \le 10$. For $40\%$ of the testdata, $n \le 3 \times 10^2$. For $60\%$ of the testdata, $n \le 10^3$. For the other $20\%$ of the testdata, it is guaranteed that $\pi'_i = i \bmod n + 1$ ($1 \le i \le n$). For $100\%$ of the testdata, $1 \le n \le 2 \times 10^5$, $0 \le k \le n$. Translated by ChatGPT 5