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;
using pii = pair<int, int>;
using ll = long long;
int n, k;
vector<pii> a;
bool answer_check = false;
void input() {
  cin >> n >> k;
  a.resize(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i].first;
    a[i].second = i;
  }
}
void output() {
  if (answer_check) {
    cout << "YES\n";
    for (pii ans : a) cout << ans.first << " ";
  } else
    cout << "NO";
}
void process() {
  bool color_check = false;
  int color = 1;
  sort(a.begin(), a.end());
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    if (i != 0 && a[i - 1].first != a[i].first) {
      if (cnt > k) return;
      for (int j = i - 1; j >= i - cnt; j--) {
        a[j].first = color;
        if (color % k == 0) color_check = true;
        color = (color % k) + 1;
      }
      cnt = 0;
    }
    cnt += 1;
  }
  if (cnt > k) return;
  for (int j = n - 1; j >= n - cnt; j--) {
    a[j].first = color;
    if (color % k == 0) color_check = true;
    color = (color % k) + 1;
  }
  if (!color_check) return;
  answer_check = true;
  sort(a.begin(), a.end(),
       [](const pii &a, const pii &b) -> bool { return a.second < b.second; });
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  input();
  process();
  output();
  return 0;
}
