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)

#include    <stdio.h>
#include    <string.h>
#include    <math.h>

int main(void)
{
    int n, k;
    int	a[200000] = { 0, };

    if (fscanf(stdin, "%d %d", &n, &k) == EOF) {
	return 1;
    }

    for (int i = 0; i < n; i++) {
	if (fscanf(stdin, "%d", a+i) == EOF) {
	    return 1;
	}
    }

    for (int j = 0; j < k; j++) {
	int b[200000] = { 0, };

	for (int i = 0; i < n; i++) {
	    for (int d = ceil(i - a[i] - 0.5); d <= floor(i + a[i] + 0.5); d++) {
		if (d < 0)
		    continue;
		if (d > 200000)
		    break;
		b[d]++;
	    }
	}
	memcpy(a, b, sizeof a);
    }

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