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>

int main(){
    int i, ii, iii;
    int a[200000], s[200000];
    int n, k;

    scanf("%d%d", &n, &k);
    
    for(i = 0;i < n;i++){
        scanf("%d", &a[i]);
    }

    for(i = 0;i < k;i++){
        for(ii = 0;ii < n;ii++){
            int index = 0;
            for(iii = 0;iii < ii;iii++){
                if(a[ii - iii] - iii >= 0)  index++;
            }
            if(a[ii] > 0) index++;
            for(iii = ii;iii < n;iii++){
                if(a[ii + iii] - iii >= 0) index++;
            }
            s[ii] = index;
        }
        for(ii = 0;ii < n;ii++){
            a[ii] = s[ii];
        }
    }

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

    return 0;
}