Posterized

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Professor Ibrahim has prepared the final homework for his algorithm’s class. He asked his students to implement the Posterization Image Filter.

Their algorithm will be tested on an array of integers, where the $\mathrm{ii-th\; integer\; represents\; the\; color\; of\; the ii-th\; pixel\; in\; the\; image.\; The\; image\; is\; in\; black\; and\; white,\; therefore\; the\; color\; of\; each\; pixel\; will\; be\; an\; integer\; between\; 0\; and\; 255\; (inclusive).}$

To implement the filter, students are required to divide the black and white color range [0, 255] into groups of consecutive colors, and select one color in each group to be the group’s key. In order to preserve image details, the size of a group must not be greater than $\mathrm{kk,\; and\; each\; color\; should\; belong\; to\; exactly\; one\; group.}$

Finally, the students will replace the color of each pixel in the array with that color’s assigned group key.

To better understand the effect, here is an image of a basking turtle where the Posterization Filter was applied with increasing $\mathrm{kk to\; the\; right.}$

To make the process of checking the final answer easier, Professor Ibrahim wants students to divide the groups and assign the keys in a way that produces the lexicographically smallest possible array.

Input

The first line of input contains two integers $\mathrm{nn and kk (1\le n\le 1051\le n\le 105, 1\le k\le 2561\le k\le 256),\; the\; number\; of\; pixels\; in\; the\; image,\; and\; the\; maximum\; size\; of\; a\; group,\; respectively.}$

The second line contains $\mathrm{nn integers p1,p2,\dots ,pnp1,p2,\dots ,pn (0\le pi\le 2550\le pi\le 255),\; where pipi is\; the\; color\; of\; the ii-th\; pixel.}$

Output

Print $\mathrm{nn space-separated\; integers;\; the\; lexicographically\; smallest\; possible\; array\; that\; represents\; the\; image\; after\; applying\; the\; Posterization\; filter.}$

Examples

input

Copy

4 3 2 14 3 4

output

Copy

0 12 3 3

input

Copy

5 2 0 2 1 255 254

output

Copy

0 1 1 254 254

Note

One possible way to group colors and assign keys for the first sample:

Color $\mathrm{22 belongs\; to\; the\; group [0,2][0,2],\; with\; group\; key 00.}$

Color $\mathrm{1414 belongs\; to\; the\; group [12,14][12,14],\; with\; group\; key 1212.}$

Colors $\mathrm{33 and 44 belong\; to\; group [3,5][3,5],\; with\; group\; key 33.}$

Other groups won't affect the result so they are not listed here.

 

 

 题意： 给你n个数，每个数的key为这个所在的组别key，每组数的大小不大于k，求使最后key值组成的序列字典序最小的一组key值

 

 题解： 直接贪心，枚举每个数的前面的数，用没有被用过的最早的数做key值，就是字典序最小了

 

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