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: Runtime Error)

#include<iostream>
using namespace std;


int main() {
	int n, k;
	int a[1000];
	int count[1000];
	cin >> n >> k;
	for (int i = 1; i <= n;i++) cin >> a[i];
	
	for (int j = 0; j < k; j++) {
		for (int i = 1; i <= n; i++) count[i] = 0;
		for (int i = 1; i <= n; i++) {
			
			for (int l = i - a[i]; l <= i + a[i]; l++) {
				if ((l > 0) && (l < n + 1)) {
					count[l]++; 
				}
			}
			
		}
		for(int i = 1; i <= n; i++) a[i] = count[i];
	}
	for (int i = 1; i <= n; i++) cout << a[i] << " ";
	return 0;
}