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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

# imos法
# 長さNの1次元配列において、「ある連続する区間に、ある数vを足す」という操作をK回繰り返した結果を高速で求める

# 初期入力
import sys
input = sys.stdin.readline
N,K = (int(i) for i in input().split())
A = list(map(int, input().split()))


l =0
r =N
cumulative_sum =[0]*N
#操作数が電球の数より多いとき
if N <=K:
    A=[N]*N
# imos法
else:
    for j in range(K):
        B =[0]*(N+1)
        for i in range(N):
            index =A[i]
            if i-index <0:
                l=0
            else:
                l =i -index
            if i +index +1 >=N:
                r =N 
            else:
                r =i +index +1
            B[l] +=1 
            B[r] -=1
        #累積和(imos法) 
        cumulative_sum[0] =B[0]       
        for i in range(1,N):
            cumulative_sum[i] =cumulative_sum[i-1] +B[i]

        A =cumulative_sum
        if sum(A) ==N*N:
            print(*A)
            sys.exit(0)
        cumulative_sum =[0]*N
    
print(*A)