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 C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>

#define max(a, b) ((int)(a) > (int)(b) ? (a) : (b))
#define min(a, b) ((int)(a) > (int)(b) ? (b) : (a))

int main(void)
{
    int N, K;
    scanf("%d %d", &N, &K);

    int A[N + 1], lamp[N + 1];
    for(int i = 0; i < N; i++)
    {
        scanf("%d", &A[i]);
    }

    for(int i = 0; i < min(K, 40); i++)
    {
        for(int j = 0; j < N + 1; j++) { lamp[j] = 0; }
        for(int j = 0; j < N; j++)
        {
            lamp[max(0, j - A[j])] += 1;
            lamp[min(N, j + A[j] + 1)] -= 1;
        }

        for(int j = 1; j < N + 1; j++) { lamp[j] += lamp[j - 1]; }
        for(int j = 0; j < N + 1; j++) { A[j] = lamp[j]; }
    }

    for(int i = 0; i < N; i++)
    {
        printf("%d ", A[i]);
    }
    printf("\n");
}