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.
def solve(n,k,ar):
    ind = []
    track = [-1] * (n)
    track[0] = 0
    for i in range(n):
        ind.append(i)




    zipped_lists = zip(ar, ind)
    sorted_pairs = sorted(zipped_lists)
    tuples = zip(*sorted_pairs)
    ar, ind = [list(tuple) for tuple in tuples]

    maxi = 0
    cnt = 1
    for i in range(n - 1):
        if ar[i] == ar[i + 1]:
            cnt += 1
        else:
            maxi = max(maxi, cnt)
            cnt = 1
    maxi = max(maxi,cnt)
    if maxi > k:
        print('NO')
        return

    for i in range(n):
        track[i] = (i-1)%k + 1


    ans = [0] * (n)

    for i in range(n):
        ans[ind[i]] = track[i]

    print('YES')
    print(" ".join(map(str,ans)))









if __name__ == '__main__':
    n,k = map(int,input().split())
    ar = list(map(int,input().split()))

    solve(n,k,ar)