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.
import sys

def result(n, k, lstN):
    if k > n:
        print("NO")
        return
    dicNum = {}
    dicCur = {}
    res = []
    mx = 1

    for i in range(n):
        if lstN[i] not in dicCur:
            dicCur[lstN[i]] = 1
            res.append(1)
        else:
            if dicCur[lstN[i]] == k:
                print("NO")
                return
            else:
                dicCur[lstN[i]] += 1
                res.append(dicCur[lstN[i]])
                mx = max(mx, dicCur[lstN[i]])
        if res[i] not in dicNum:
            dicNum[res[i]] = 1
        else:
            dicNum[res[i]] += 1
    if mx < k:
        distant = 1
        for i in range(n):
            if distant <= k-mx:
                if dicNum[res[i]] > 1:
                    dicNum[res[i]] -= 1
                    res[i] = mx+distant
                    mx += 1

            else:
                break
    if mx == k:
        print("YES")
        for i in res:
            print(i, end=" ")
    else:
        print("NO")



if __name__ == '__main__':
    tempOne = sys.stdin.readline().split(" ")
    n, k = int(tempOne[0]), int(tempOne[1])
    tempTwo = sys.stdin.readline().split(" ")
    lstN = list(map(lambda x: int(x), tempTwo))
    result(n, k, lstN)
 		 	 	      	  						      	