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.
class CodeforcesTask1102BSolution:
    def __init__(self):
        self.result = ''
        self.n_k = []
        self.values = []

    def read_input(self):
        self.n_k = [int(x) for x in input().split(" ")]
        self.values = [int(x) for x in input().split(" ")]

    def process_task(self):
        colorings = [{self.values[x]} for x in range(self.n_k[1])]
        colors = [0] * self.n_k[0]
        for x in range(self.n_k[1]):
            colors[x] = x + 1
        can_ = True
        #print(colorings)
        for x in range(self.n_k[1], self.n_k[0]):
            has_ = False
            for y in range(self.n_k[1]):
                #print(x, y, colorings)
                if self.values[x] not in colorings[y]:
                    colorings[y].add(self.values[x])
                    colors[x] = y + 1
                    has_ = True
                    break
            if not has_:
                can_ = False
                break
        if can_:
            self.result = "YES\n{0}".format(" ".join([str(x) for x in colors]))
        else:
            self.result = "NO"

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask1102BSolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())
