P6934 [ICPC 2017 WF] Posterize

 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 $d (1 \le d \le 256)$ , the number of distinct red values that occur in the original image, and $k (1 \le k \le d)$ , 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 $r (0 \le r \le 255)$ and $p (1 \le p \le 2^{26}),$ 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.

Time limit: 2 s, Memory limit: 512 MB.