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>
int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  size_t n, k;
  std::cin >> n >> k;
  if (n < k) {
    std::cout << "NO\n";
    return 0;
  }
  std::vector<size_t> a(n);
  for (size_t i = 0; i < n; ++i) {
    std::cin >> a[i];
    a[i] -= 1;
  }
  std::vector<size_t> colors(n);
  size_t ptr = 0;
  bool ok = true;
  for (size_t i = 0; i < 5000; ++i) {
    size_t count = 0;
    for (size_t j = 0; j < n; ++j) {
      if (a[j] != i) {
        continue;
      }
      colors[j] = ptr;
      ptr += 1;
      if (ptr == k) {
        ptr = 0;
      }
      count += 1;
    }
    if (count > k) {
      ok = false;
      break;
    }
  }
  if (!ok) {
    std::cout << "NO\n";
  } else {
    std::cout << "YES\n";
    for (size_t c : colors) {
      std::cout << c + 1 << ' ';
    }
    std::cout << '\n';
  }
}
