Priority Queue 2

AtCoder

IDarc139_d

Time2000ms

Memory256MB

Difficulty—

You are given a multiset of integers with $N$ elements: $A=\lbrace A_1,A_2,...,A_N \rbrace$. It is guaranteed that every element of $A$ is between $1$ and $M$ (inclusive). Let us repeat the following operation $K$ times. * Choose an integer between $1$ and $M$ (inclusive) and add it to $A$. Then, delete the $X$\-th smallest value in $A$. Here, the $X$\-th smallest value in $A$ is the $X$\-th value from the front in the sequence of the elements of $A$ sorted in non-decreasing order. There are $M^K$ ways to choose an integer $K$ times between $1$ and $M$. Assume that, for each of these ways, we have found the sum of the elements of $A$ after the operations with the corresponding choices. Find the sum, modulo $998244353$, of the $M^K$ values computed. ## Constraints * $1 \le N,M,K \le 2000$ * $1 \le X \le N+1$ * $1 \le A_i \le M$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $K$ $X$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

2 4 2 1
1 3

Output #1

99

We start with $A={1,3}$. Here is an example of how we do the operations.

*   Add $4$ to $A$, making $A={1,3,4}$. Then, delete the $1$\-st smallest value, making $A={3,4}$.
    
*   Add $3$ to $A$, making $A={3,3,4}$. Then, delete the $1$\-st smallest value, making $A={3,4}$.
    

In this case, the sum of the elements of $A$ after the operations is $3+4=7$.

Input #2

5 9 6 3
3 7 1 9 9

Output #2

15411789

API Response (JSON)

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