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.
function calc(n, k, a) {
  if (k > n) {
    print("NO");
    return;
  }
  
  var dict = {};
  a.map(elem => {
    if (dict[elem]) {
      dict[elem]++;
    } else {
      dict[elem] = 1;
    }
  });
  
  // count of same elem > colors
  if (Math.max(...Object.keys(dict).map(key => dict[key])) > k) {
    print("NO");
    return;
  }
  
  var res = a
    .map((elem, index) => {
      return {
        val: elem,
        index: index
      }
    })
    .sort((a, b) => a.val - b.val)
    .map((elem, i) => {
      return {
        val: elem.val,
        index: elem.index,
        color: i % k + 1
        
      }
    })
    .sort((a, b) => a.index - b.index)
    .map(elem => elem.color)
    
  print("YES");
  print(res.join(" "));
  
}

var nk = readline().split(" ");
var n = parseInt(nk[0]);
var k = parseInt(nk[1]);

var a = readline().split(" ");

calc(n, k, a);