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() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int n, k;
  cin >> n >> k;
  long long int arr[n], ans[n];
  for (long long int i = 0; i < n; i++) cin >> arr[i];
  set<long long int> colors[k + 1];
  set<long long int> marked;
  set<pair<long long int, long long int> > coor_col[k + 1];
  for (long long int i = 1; i <= k; i++) marked.insert(i);
  for (long long int i = 0; i < n; i++) {
    bool flag = 1;
    for (long long int j = 1; j <= k; j++) {
      if (colors[j].find(arr[i]) == colors[j].end()) {
        flag = 0;
        colors[j].insert(arr[i]);
        coor_col[j].insert(make_pair(arr[i], i));
        ans[i] = j;
        marked.erase(j);
        break;
      }
    }
    if (flag) {
      cout << "NO\n";
      return 0;
    }
  }
  for (auto it : marked) {
    int co = 0;
    for (long long int i = 1; i <= k; i++) {
      if (coor_col[i].size() > 1) {
        set<pair<long long int, long long int> > temp;
        bool flag = 0;
        while (!coor_col[i].empty()) {
          pair<long long int, long long int> x = (*coor_col[i].begin());
          coor_col[i].erase(x);
          colors[i].erase(x.first);
          if (colors[it].find(x.first) == colors[it].end()) {
            ans[x.second] = it;
            coor_col[it].insert(x);
            colors[it].insert(x.first);
            co = 1;
            flag = 1;
            break;
          } else {
            temp.insert(x);
            colors[i].insert(x.first);
          }
        }
        for (auto it : temp) coor_col[i].insert(it);
        if (flag) break;
      }
    }
    if (!co) {
      cout << "NO\n";
      return 0;
    }
  }
  cout << "YES\n";
  for (long long int i = 0; i < n; i++) cout << ans[i] << " ";
  cout << endl;
  return 0;
}
