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>
#include<string>
#include<algorithm>
#include<numeric>
#include<stack>
#include<queue>
#include<unordered_map>
#include<cmath>
#include<utility>

using ULL = unsigned long long;
using LL = long long;
using String = std::string;
using Ints = std::vector<int>;
using Doubles = std::vector<double>;
using Bools = std::vector<bool>;
using Strings = std::vector<std::string>;
using ULLs = std::vector<ULL>;
using LLs = std::vector<LL>;

// pythonのdictionary相当
template <typename T1, typename T2>
using Dict = std::unordered_map<T1,T2>;



int main(void) {
    int n, k;
    std::cin >> n >> k;
    Ints A(n);
    for(int i=0;i<n;i++){
        int _a;
        std::cin >> _a;
        A[i] = _a;
    }

    for(int i=0;i<k;i++){
        Ints B(n+1, 0);
        for(int j=0;j<n;j++){
            B[std::max(0, j-A[j])]++;
            B[std::min(n, j+A[j]+1)]--;
        }
        for(int j=0;j<n;j++){
            B[j+1]+=B[j];
        }
        A=B;
    }

    for(int i=0;i<n;i++){
        std::cout << A[i] << " ";
    }
    std::cout << std::endl;

    return 0;
}