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: Time Limit Exceeded)

#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")

#include <stdio.h>

int main(void)
{
    int n, k, in, i, j, t;

    scanf("%d %d", &n, &k);
    int a[n], b[n];

    for(i = 0; i < n; i++)
        a[i] = 0;

    for(i = 0; i < n; i++)
    {
        scanf("%d", &in);
        t = i + in < n ? i+in+1:n;
        for(j = 0 > i - in ? 0: i-in; j < t; j++)
            a[j]++;
    }

    while(--k)
    {
        for(i = 0; i < n; i++)
        {
            b[i] = a[i];
            a[i] = 0;
        }

        for(i = 0; i < n; i++)
        {
            t = i + b[i] < n ? i+b[i]+1:n;
            for(j = 0 > i - b[i] ? 0: i-b[i]; j < t; j++)
                a[j]++;
        }
    }

    for(i = 0; i < n; i++)
        printf("%d ", a[i]);

    return 0;
}