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 <bits/stdc++.h>

#define rep(i,n) for(int i=0;i<(n);++i)
using namespace std;
using ll = long long;
using P = pair<int, int>;

int main() {
	ll n,k;
	cin >> n >> k;
	vector<int> a(n);
	rep(i,n) cin >> a[i];
	while(--k >= 0) {
		vector<int> dp(n);
		rep(i,n) {
			int d = a[i];
			for (int j = -d+i;j<=d+i;j++) {
				if (j >= 0 && j < n) {
					dp[j]++;
				}
			}
		}
		rep(i,n) {
			a[i] = dp[i];
		}
	}
	rep(i,n) {
		cout << a[i];
		if (i < n-1)
			cout << " ";
		else
			cout << endl;
	}
	return 0;
}