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: Accepted)

# coding: utf-8
import numpy as np
from numba import b1, i8, njit, types


@njit(types.Tuple((i8[:], b1))(i8[:]), cache=True)
def f(A):
    n = len(A)
    ret = np.zeros_like(A)
    for x, p in enumerate(A):
        ret[max(0, x-p)] += 1
        if x+p+1 < n:
            ret[x+p+1] -= 1

    satulated = True
    for i in range(1, n):
        ret[i] += ret[i-1]
        satulated &= ret[i] == n
    return ret, satulated


def solve(*args: str) -> str:
    n, k = map(int, args[0].split())
    A = np.array(tuple(map(int, args[1].split())))

    for _ in range(k):
        A, satulated = f(A)
        if satulated:
            break

    return ' '.join(map(str, A))


if __name__ == "__main__":
    print(solve(*(open(0).read().splitlines())))