We have N bulbs arranged on a number line, numbered 1 to N from left to right. Bulb i is at coordinate i.

Each bulb has a non-negative integer parameter called intensity. When there is a bulb of intensity d at coordinate x, the bulb illuminates the segment from coordinate x-d-0.5 to x+d+0.5. Initially, the intensity of Bulb i is A_i. We will now do the following operation K times in a row:

* For each integer i between 1 and N (inclusive), let B_i be the number of bulbs illuminating coordinate i. Then, change the intensity of each bulb i to B_i.



Find the intensity of each bulb after the K operations.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq K \leq 2 \times 10^5
* 0 \leq A_i \leq N

Input

Input is given from Standard Input in the following format:


N K
A_1 A_2 \ldots A_N


Output

Print the intensity A{'}_i of each bulb i after the K operations to Standard Output in the following format:


A{'}_1 A{'}_2 \ldots A{'}_N

Output

Print the intensity A{'}_i of each bulb i after the K operations to Standard Output in the following format:


A{'}_1 A{'}_2 \ldots A{'}_N

Examples

Input

5 1
1 0 0 1 0


Output

1 2 2 1 2


Input

5 2
1 0 0 1 0


Output

3 3 4 4 3
from decimal import *
FAST_IO = 1
if FAST_IO:
    import io, sys, atexit
    rr = iter(sys.stdin.read().splitlines()).next
    sys.stdout = _OUTPUT_BUFFER = io.BytesIO()
    @atexit.register
    def write():
        sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
else:
    rr = raw_input
rri = lambda: int(rr())
rrm = lambda: map(int, rr().split())



def solve(N, K, A):
    def update():
        new_A = [0]*N
        end_idx = [0]*N
        num_act = 0
        num_max = 0
        for i in range(N):
            end_idx[min(i+A[i], N-1)]+=1
            num_act+=1
            new_A[i] = num_act
            num_act-=end_idx[i]
        end_idx = [0]*N
        num_act = 0
        num_max = 0
        for i in range(N-1, -1, -1):
            tmp = A[i]
            new_A[i]+= num_act
            if new_A[i] == N:
                num_max+=1
            if A[i]>0:
                num_act += 1
                end_idx[max(0,i-tmp)]+=1
            num_act -= end_idx[i]
        return new_A, num_max
    for _ in range(K):
        A, num_max = update()
        if num_max == N:
            return [str(n) for n in A]
    return [str(n) for n in A]
    



N, K = rrm()
A = rrm()
ans = solve(N, K, A)
print(' '.join(ans))
