B - Build Tree

B - Build Tree

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:

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 ≤ k ≤200000,2 ≤ p≤ 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.

Sample Input

5 2 3 10
1 2 3 4 5

6

Time limit——1500 ms
Memory limit——65536 kB

题意：
现有 k 条线，要用这些线构建一颗 m 层的 n 叉树（必须是满的树），要求求出根节点到 其他节点距离之和的最小值 ，由于这个最小值可能太大，所以要求答案取余 p ，注：每条线仅一条，且题目保证线够用
分析：
原理很好想，计算根节点到其余所有节点的距离时越靠近根节点的线段重复计算的次数越多，比如现有4层的二叉树，边长分别为分别是1，2，3

我们先将根节点到每个点的距离相加，计算一下最终答案
公式为：(1+2+3)*8 + (1+2)*4 + (1)*2 = 62
将每一层的边出现次数统计一下得
1 ：(8+4+2)/2 = 7 = 1+2+4
2 ：(8+4)/4