Problem Description

You need to construct a full $n$-ary tree(n叉树) with $m$ layers.All the edges in this tree have a weight.But this weight cannot be chosen arbitrarily you can only choose from set $S$，the size of $S$ is $k$，each element in the set can only be used once.Node 0 is the root of tree.

We use $d(i)$ for the distance from root to node $i$.Our goal is to minimize the following expression:
$$
\min \sum_{i=0}^N{d(i)}
$$


Please find the minimum value of this expression and output it.Because it may be a big number,you should output the answer modul $p$.

Input

The input file contains 2 lines.

The first line contains 4 integers,these respectively is $k$,$m$,$n$,$p$。(2 $\leq$ $k$ $\leq $200000,2 $ \leq $ $p$$ \leq $ $10^{15}$)

The second line contains $k$ integers,represent the set $S$，the elements in the set guarantee less than or equal to $10^{15}$.

We guarantee that $k$ is greater than or equal to the number of edges.

Output

The output file contains an integer.represent the answer.

5 2 3 10
1 2 3 4 5

6