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 n, k, t;
  vector<int> arr;
  unordered_map<int, int> map;
  unordered_map<int, vector<int>> color_arr;
  scanf("%d %d ", &n, &k);
  for (int i = 0; i < n; i++) {
    scanf("%d", &t);
    arr.push_back(t);
    if (map.find(t) == map.end()) {
      map[t] = 1;
      color_arr[t] = vector<int>();
    } else {
      map[t] += 1;
    }
  }
  bool flag = false;
  for (auto v : map) {
    if (v.second > k) {
      flag = true;
      break;
    }
  }
  if (flag) {
    printf("NO\n");
  } else {
    printf("YES\n");
    int used_color = 1;
    for (int a : arr) {
      if (used_color <= k) {
        printf("%d ", used_color);
        color_arr[a].push_back(used_color);
        used_color++;
      } else {
        while (true) {
          if (find(color_arr[a].begin(), color_arr[a].end(), map[a]) !=
              color_arr[a].end()) {
            map[a]--;
          } else {
            color_arr[a].push_back(map[a]);
            printf("%d ", map[a]);
            map[a]--;
            break;
          }
        }
      }
    }
  }
  return 0;
}
