Array K-Coloring
Description
You 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.
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 $a$.
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.
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.
Samples
4 2
1 2 2 3
YES
1 1 2 2
5 2
3 2 1 2 3
YES
2 1 1 2 1
5 2
2 1 1 2 1
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.