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: Wrong Answer)

import sys

def solve():
    input = sys.stdin.readline
    N, K = map(int, input().split())
    A = [int(a) for a in input().split()]
    if K >= 20: A = [N] * N
    else:
        for k in range(K):
            nextL = [0] * (N + 1)
            for i, a in enumerate(A):
               left = max(0, i - a)
               right = min(N, i + a + 1)
               nextL[left] += 1
               nextL[right] -= 1
            #print(nextL)
            A[0] = nextL[0]
            for i in range(1, N):
                A[i] = A[i-1] + nextL[i]
    print(*A, sep=" ")
    return 0

if __name__ == "__main__":
    solve()