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B. Array K-Coloring

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given an array $$$a$$$ consisting of $$$n$$$ integer numbers.

You have to color this array in $$$k$$$ colors in such a way that:

- Each element of the array should be colored in some color;
- For each $$$i$$$ from $$$1$$$ to $$$k$$$ there should be at least one element colored in the $$$i$$$-th color in the array;
- For each $$$i$$$ from $$$1$$$ to $$$k$$$ all elements colored in the $$$i$$$-th color should be distinct.

Obviously, such coloring might be impossible. In this case, print "NO". Otherwise print "YES" and any coloring (i.e. numbers $$$c_1, c_2, \dots c_n$$$, where $$$1 \le c_i \le k$$$ and $$$c_i$$$ is the color of the $$$i$$$-th element of the given array) satisfying the conditions above. If there are multiple answers, you can print any.

Input

The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 5000$$$) — the length of the array $$$a$$$ and the number of colors, respectively.

The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 5000$$$) — elements of the array $$$a$$$.

Output

If there is no answer, print "NO". Otherwise print "YES" and any coloring (i.e. numbers $$$c_1, c_2, \dots c_n$$$, where $$$1 \le c_i \le k$$$ and $$$c_i$$$ is the color of the $$$i$$$-th element of the given array) satisfying the conditions described in the problem statement. If there are multiple answers, you can print any.

Examples

Input

4 2 1 2 2 3

Output

YES 1 1 2 2

Input

5 2 3 2 1 2 3

Output

YES 2 1 1 2 1

Input

5 2 2 1 1 2 1

Output

NO

Note

In the first example the answer $$$2~ 1~ 2~ 1$$$ is also acceptable.

In the second example the answer $$$1~ 1~ 1~ 2~ 2$$$ is also acceptable.

There exist other acceptable answers for both examples.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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