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)

def main():
    N,K = map(int,input().split())
    A = list(map(int,input().split()))
    dict = {}
    temp = {}
    ruiseki = {}
    for i in range(N):
        dict[i+1] = A[i]
        temp[i+1] = 0
        ruiseki[i+1] = 0

    dict[N+1] = 0
    temp[N+1] = 0
    ruiseki[N+1] = 0

    for j in range(K):
        for m in range(1,N+1):
            if dict[m] < N:
                break
            else:
                if m == N:
                    ans = list(dict.values())
                    ans2 = str(ans[0])
                    for i in range(1,N):
                        ans2 += (' ' + str(ans[i]))
                    return(ans2)
                continue

        for h in range(1,N+1):
            temp2 = dict[h]
            if h - temp2 <= 0:
                temp[1] += 1
            else:
                temp[h - temp2] += 1

            if h+temp2+1 > N:
                temp[N+1] -= 1
            else:
                temp[h+temp2+1] -= 1

        for n in range(1,N+2):
            for k in range(1,n+1):
                ruiseki[n] += temp[k]


        for i in range(1,N+2):
            dict[i] = ruiseki[i]
            temp[i] = 0
            ruiseki[i] = 0

    ans = list(dict.values())
    ans2 = str(ans[0])
    for i in range(1,N):
        ans2 += (' ' + str(ans[i]))
    return(ans2)

print(main())