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 <iostream>
#include <vector>

using namespace std;

int main(){
    int N, K;
    cin >> N >> K;

    vector<int> a(N);
    for(int i=0; i<N; ++i){
        cin >> a[i];
    }

    if(N >= K){
        for(int n=0; n<K; ++n){
            vector<int> delta(N, 0);
            for(int i=0; i<N; ++i){
                int power = a[i];

                int MIN = max(0, i - power);
                int MAX = min( N-1, i + power);

                if(power > 0){
                    for(int j=MIN; j<i; ++j){
                        delta[j]++;
                    }

                    for(int j=i+1; j<=MAX; ++j){
                        delta[j]++;
                    }
                }
            }
            for(int i=0; i<N; ++i){
                delta[i]++;
            }

            swap(a, delta);
        }
    }else{
        for(int i=0; i<N; ++i){
            a[i] = N;
        }
    }

    for(int i=0; i<N; ++i){
        cout << a[i] << " ";
    }


    return 0;
}