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 <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < n; i++)
#define all(v) v.begin(), v.end()
    
int main(){
    int n,k;
    cin >> n >> k;
    vector <int> A(n);
    rep(i,n) cin >> A[i];

    if(n == 1){
        cout << min(n,k) << endl;
    }

    else{
        rep(l,min(50,k)){
            vector <int> B(n,0);
            for(int i=0; i<n; i++){
                int l = max(0,i-A[i]);
                int r = min(i+A[i],n-1);
                B[l] ++;
                if(B[r+1]<n){
                    B[r+1]--;
                }
            }
    
            for(int i=1; i<n; i++) B[i] += B[i-1];//B complete

            rep(i,n){
                A[i] = B[i];//new A
            }        
        }
    }

    rep(i,n){
        if(i==n-1){
            if(A[i]>n){
                cout << n << endl;
            }
            else{
                cout << A[i]<<endl;
            }
        }
        else{
            if(A[i]>n){
                cout << n << endl;
            }
            else{
                cout << A[i] << " ";
            }
        }
    }
}