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>
#include <math.h>
#define ALL(a)    a.begin(), a.end()
using namespace std;

int main() {
long long int N, K;cin >> N >> K;
vector<long long int> P;
vector<long long int> p;
bool C;

P.resize(N);p.resize(N);

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


for(int m = 0; m < K; m++){

for(int i = 0; i < N; i++){
long int Q = i + 1 - P[i];
if(Q < 1)Q = 1;
while (1 <= Q && Q <= i + 1 + 0.5 + P[i]){
p[Q - 1]++;
Q++;}
}

C = 1;

for(int i = 0; i < N; i++){
P[i] = p[i];
if(P[i] <= N)C = 0;
p[i] = 0;
}
if(C)break;
}

if(!C){
for(int i = 0; i < N; i++){
cout << P[i] << " ";
}
}

if(C){
for(int i = 0; i < N; i++){
cout << N << " ";
}
}

}