Problem:
Score : 500 points

Problem Statement

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

Sample Input 1

5 1
1 0 0 1 0

Sample Output 1

1 2 2 1 2

Initially, only Bulb 1 illuminates coordinate 1, so the intensity of Bulb 1 becomes 1 after the operation.
Similarly, the bulbs initially illuminating coordinate 2 are Bulb 1 and 2, so the intensity of Bulb 2 becomes 2.

Sample Input 2

5 2
1 0 0 1 0

Sample Output 2

3 3 4 4 3

Solution in PyPy3 (7.3.0) (judge verdict: Runtime Error)


N,K=map(int,input().split())
A= list(map(int,input().split()))
new_A = A
len_A=len(A)
count_list = [0]*len_A
K_list=range(K)
A_list=range(len_A)
for i in K_list:
    for j in A_list:
        if(new_A[j]!=0):
            low_posi=j-new_A[j]
            if(low_posi<0):
                low_posi=0
            high_posi = j+new_A[j]
            if(high_posi>len_A):
                high_posi=len_A+1
            for k in range(low_posi,high_posi):
                count_list[k] += 1
        else:
            count_list[j]+=1
    new_A=count_list
    count_list = [0]*len_A
for s in new_A:
    print(str(s)+" ", end ="")
print("")