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, ... c_n, where 1 ≤ c_i ≤ 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 ≤ k ≤ n ≤ 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, ..., a_n (1 ≤ a_i ≤ 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, ... c_n, where 1 ≤ c_i ≤ 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.
#include <bits/stdc++.h>
void load(int n, std::vector<int> *v) {
  for (int i = 0; i < n; ++i) {
    int a;
    std::cin >> a;
    (*v).push_back(a);
  }
}
void init_freq(const std::vector<int> &v, std::map<int, int> *freq) {
  for (int elem : v) {
    (*freq)[elem]++;
  }
}
bool is_valid(const std::map<int, int> &freq, int k) {
  for (auto f : freq) {
    if (f.second > k) {
      return false;
    }
  }
  return true;
}
void set_colors(int k, const std::map<int, int> &freq,
                std::map<int, int> *colors) {
  int used_colors = 0;
  for (auto f : freq) {
    used_colors += f.second;
    (*colors)[f.first] = std::min(used_colors, k);
  }
}
void output(std::map<int, int> *colors, const std::vector<int> &v) {
  for (int elem : v) {
    std::cout << (*colors)[elem]-- << " ";
  }
  std::cout << std::endl;
}
int main() {
  int n, k;
  std::cin >> n >> k;
  std::vector<int> v;
  load(n, &v);
  std::map<int, int> freq;
  init_freq(v, &freq);
  if (is_valid(freq, k)) {
    std::cout << "YES" << std::endl;
  } else {
    std::cout << "NO" << std::endl;
    return 0;
  }
  std::map<int, int> colors;
  set_colors(k, freq, &colors);
  output(&colors, v);
  return 0;
}
