# 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 $r_1, \ldots
, r_ n$, and $k$
allowed integers $v_1, \ldots ,
v_ k$, the sum of squared errors is defined
as

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.

## Input

The first line of the input contains two integers $d$ ($1 \leq d \leq 256$), the number of distinct red values that occur in the original image, and $k$ ($1 \leq k \leq d$), 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 $r$ ($0 \leq r \leq 255$) and $p$ ($1 \leq p \leq 2^{26}$), 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.

## Output

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

Sample Input 1 | Sample Output 1 |
---|---|

2 1 50 20000 150 10000 |
66670000 |

Sample Input 2 | Sample Output 2 |
---|---|

2 2 50 20000 150 10000 |
0 |

Sample Input 3 | Sample Output 3 |
---|---|

4 2 0 30000 25 30000 50 30000 255 30000 |
37500000 |