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 (Clang 10.0.0) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

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

	scanf("%d", &n);
	scanf("%d", &k);

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

	int mode = 0;
	for (int i = 0; i < k; i++) {
		for (int j = 0; j < n; j++) {
			for (int x = 0; x < n; x++) {
				if (j - a[j] <= x && x <= j + a[j]) {
					b[x]++;
				}
			}
		}
		for (int i = 0; i < n; i++) {
			a[i] = b[i];
			b[i] = 0;
		}
	}

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

	return 0;
}