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 suitable():
    global arr, k
    arrs = sorted(arr)
    j = 0
    for i in range(len(arrs) - 1):
        if arrs[i] == arrs[i + 1]:
            j += 1
        else:
            j = 0
        if j >= k:
            return False
    return True
        
n, k = map(int, input().split())
arr = [int(x) for x in input().split()]
colors = {}
for i in range(1, k + 1):
    colors[i] = set()
    
if not suitable():
    print('NO')
else:
    print('YES')
    arr2 = sorted(arr)
    p = 0
    d = {}
    for i in set(arr):
        d[i] = set()
    for i in arr2:
        d[i].add(p % k + 1)
        p += 1
    for i in arr:
        print(d[i].pop(), end=' ')

