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>
using namespace std;
int main(int argc, char const *argv[]) {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  int a[n];
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  map<int, vector<int>> m;
  set<int> s;
  int cnt = 1;
  vector<int> ans;
  for (int i = 0; i < n; ++i) {
    if (m[a[i]].size() == 0 && s.size() < k) {
      ans.push_back(s.size() + 1);
      m[a[i]].push_back(s.size() + 1);
      s.insert(ans[i]);
    } else if (m[a[i]].size() == k) {
      cout << "NO";
      return 0;
    } else {
      int p;
      sort(m[a[i]].begin(), m[a[i]].end());
      for (p = 0; p < m[a[i]].size(); ++p) {
        if (m[a[i]][p] != p + 1) break;
      }
      if (s.size() < k) {
        ans.push_back(s.size() + 1);
        m[a[i]].push_back(s.size() + 1);
        p = s.size() + 1;
        s.insert(p);
        continue;
      }
      ans.push_back(p + 1);
      m[a[i]].push_back(p + 1);
      s.insert(p + 1);
    }
  }
  if (s.size() != k) {
    cout << "NO";
    return 0;
  }
  cout << "YES\n";
  for (int i = 0; i < n; ++i) cout << ans[i] << " ";
  return 0;
}
