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: Wrong Answer)

import sys, re
from math import ceil, floor, sqrt, pi, factorial, gcd
from copy import deepcopy
from collections import Counter, deque
from heapq import heapify, heappop, heappush
from itertools import accumulate, product, combinations, combinations_with_replacement
from bisect import bisect, bisect_left
from functools import reduce
from decimal import Decimal, getcontext
# input = sys.stdin.readline 
def i_input(): return int(input())
def i_map(): return map(int, input().split())
def i_list(): return list(i_map())
def i_row(N): return [i_input() for _ in range(N)]
def i_row_list(N): return [i_list() for _ in range(N)]
def s_input(): return input()
def s_map(): return input().split()
def s_list(): return list(s_map())
def s_row(N): return [s_input for _ in range(N)]
def s_row_list(N): return [s_list() for _ in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
def lcm(a, b): return a * b // gcd(a, b)
sys.setrecursionlimit(10 ** 6)
INF = float('inf')
MOD = 10 ** 9 + 7

def main():
    n, k = i_map()
    num_list = i_list()

    ans_list = [0] * n

    if k > 10**2:
        print([n]*n)
        exit()

    for i in range(k):
        if i % 2 != 0:
            if ans_list.count(n) == n:
                print(*ans_list)
                exit()
            num_list = [0] *n  
            for j in range(n):
                for w in range(ans_list[j]+1):
                    if w == 0:
                        num_list[j] += 1
                    else:
                        if j + w < n:
                            num_list[j+w] += 1
                        if j - w >= 0:
                            num_list[j-w] += 1
        else:
            if num_list.count(n) == n:
                print(*num_list)
                exit()
            ans_list = [0] *n  
            for j in range(n):
                for w in range(num_list[j]+1):
                    if w == 0:
                        ans_list[j] += 1
                    else:
                        if j + w < n:
                            ans_list[j+w] += 1
                        if j - w >= 0:
                            ans_list[j-w] += 1

    if k % 2 == 0:
        print(*num_list)
    else:
        print(*ans_list)

if __name__ == '__main__':
    main()