You are given a permutation P_1 ... P_N of the set {1, 2, ..., N}.

You can apply the following operation to this permutation, any number of times (possibly zero):

* Choose two indices i,j (1 ≦ i < j ≦ N), such that j - i ≧ K and |P_i - P_j| = 1. Then, swap the values of P_i and P_j.



Among all permutations that can be obtained by applying this operation to the given permutation, find the lexicographically smallest one.

Constraints

* 2≦N≦500,000
* 1≦K≦N-1
* P is a permutation of the set {1, 2, ..., N}.

Input

The input is given from Standard Input in the following format:


N K
P_1 P_2 ... P_N


Output

Print the lexicographically smallest permutation that can be obtained.

Examples

Input

4 2
4 2 3 1


Output

2
1
4
3


Input

5 1
5 4 3 2 1


Output

1
2
3
4
5


Input

8 3
4 5 7 8 3 1 2 6


Output

1
2
6
7
5
3
4
8
N,K = input().split()
N,K = int(N), int(K)
P = [[int(x),i] for i,x in enumerate(input().split())]
P = sorted(P)
# [(1, 3), (2, 1), (3, 2), (4, 0)]
flag = False
i = -1
while(True):

    if P[i-1][1] - P[i][1] >= K:
        temp = P[i-1][1]
        P[i-1][1] = P[i][1]
        P[i][1] = temp
        flag = True
        
    elif i == -(len(P)-1):
        if flag == False:
            break
        i = -1
        flag = False

    else:
        i=i-1
        

       
#print(answer)
for i in sorted(P, key = lambda p:p[1]):
    print(i[0])
      
