[ICPC WF 2017-F]Posterize

内存限制：1024 MB 时间限制：2000 ms

Pixels in a digital picture can be represented with three integers in the range $0$ to $255$ that indicate the intensity of the red, green, and blue colors. To compress an image or to create an artistic effect, many photo-editing tools include a “posterize” operation which works as follows. Each color channel is examined separately; this problem focuses only on the red channel. Rather than allow all integers from $0$ to $255$ for the red channel, a posterized image allows at most $k$ integers from this range. Each pixel’s original red intensity is replaced with the nearest of the allowed integers. The photo-editing tool selects a set of $k$ integers that minimizes the sum of the squared errors introduced across all pixels in the original image. If there are $n$ pixels that have original red values $r_1,…,r_n$, and $k$ allowed integers $v_1,…,v_k$, the sum of squared errors is defined as

$\sum\limits_{i=1}^{n}\min\limits_{1 \le j \le k}(r_i-v_j)^2$.

Your task is to compute the minimum achievable sum of squared errors, given parameter $k$ and a description of the red intensities of an image’s pixels.

The first line of the input contains two integers $d(1≤d≤256)$, the number of distinct red values that occur in the original image, and $k(1≤k≤d)$, the number of distinct red values allowed in the posterized image. The remaining $d$ lines indicate the number of pixels of the image having various red values. Each such line contains two integers $r(0≤r≤255)$ and $p(1≤p≤2^{26})$, where $r$ is a red intensity value and $p$ is the number of pixels having red intensity $r$. Those $d$ lines are given in increasing order of red value.

Display the sum of the squared errors for an optimally chosen set of $k$ allowed integer values.

样例输入 1

2 1
50 20000
150 10000

样例输出 1

66670000

样例输入 2

2 2
50 20000
150 10000

样例输出 2

样例输入 3

样例输出 3

37500000

C1608 [ICPC WF 2017-F]Posterize

题目描述

输入格式

输出