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: Accepted)

#include <bits/stdc++.h>
using namespace std;
int main(){
    long long N, K;
    cin >> N >> K;
    vector<long long> A(N);
    for(int i = 0; i < N; i++) cin >> A[i];
    long long cnt = 0;
    while(1){
        cnt++;
        vector<long long> sum(N + 1, 0);
        for(int i = 0; i < N; i++){
            sum[max(0LL, i - A[i])]++;
            sum[min(N, i + A[i] + 1)]--;
        }
        for(int i = 1; i < N + 1; i++) sum[i] += sum[i - 1];
        int flag = 0;
        for(int i = 0; i < N; i++) {
            A[i] = sum[i];
            if(A[i] != N) flag = 1;
        }
        if(cnt == K) break;
        if(flag == 0) break;
    }
    for(int i = 0; i < N; i++) cout << A[i] << ' ';
    cout << endl;
}