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 N, K;
pair<int, int> arr[5003];
int colors[5003];
int main() {
  scanf("%d %d", &N, &K);
  for (int n = 0; n < N; n++) {
    int value;
    scanf("%d", &value);
    arr[n] = make_pair(value, n);
  }
  sort(arr, arr + N);
  bool possible = true;
  int maxlen = 0;
  int color = 0;
  for (int n = 0; n < N;) {
    int value = arr[n].first;
    int m = n;
    while (arr[m].first == value) m++;
    int len = m - n;
    if (K < len) {
      possible = false;
      break;
    }
    maxlen = max(maxlen, len);
    for (int i = 0; i < len; i++) {
      pair<int, int> cur = arr[n + i];
      colors[cur.second] = color + 1;
      color++;
      color %= K;
    }
    n = m;
  }
  if (possible) {
    printf("YES\n");
    for (int n = 0; n < N; n++) {
      printf("%d ", colors[n]);
    }
    printf("\n");
  } else {
    printf("NO\n");
  }
  return 0;
}
