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: Runtime Error)

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

int main() {
	int n, k,a[200000],b[200000];
	scanf("%d%d", &n, &k);

	for (int i = 0; i < n; i++) {
		scanf("%d", &a[i]);
	}
	for (int i = 0; i < k; i++) {
		int flag = 1;
		for (int j = 0; j < n; j++) {
			int l = fmaxf(0, j - a[j]);
			int r = fminf(n - 1, j + a[j]);
			b[j]++;
			if (r + 1 < n) b[r + 1]--;
		}
		for (int j = 0; j < n - 1; j++) b[j + 1] += b[j];
		for (int j = 0; j < n; j++) {
			a[j] = b[j];
			if (a[j] != n) flag = 0;
		}
		if (flag==1) break;
	}
	for (int i = 0; i < k; i++) scanf("%d", a[i]);

	return 0;
}