B. Sum of Medians

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于 2020-11-18 14:12:58 发布 · 498 阅读

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给定非递减数组和k个子数组，你需要将所有数字分成k个大小为n的子数组，使得所有子数组的中位数之和最大。输出这个最大可能的中位数之和。

https://codeforces.ml/contest/1440/problem/B

A median of an array of integers of length nn is the number standing on the ⌈n2⌉⌈n2⌉ (rounding up) position in the non-decreasing ordering of its elements. Positions are numbered starting with 11. For example, a median of the array [2,6,4,1,3,5][2,6,4,1,3,5] is equal to 33. There exist some other definitions of the median, but in this problem, we will use the described one.

Given two integers nn and kk and non-decreasing array of nknk integers. Divide all numbers into kk arrays of size nn, such that each number belongs to exactly one array.

You want the sum of medians of all kk arrays to be the maximum possible. Find this maximum possible sum.

Input

The first line contains a single integer tt&n