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 "bits/stdc++.h"

using namespace std;

void Main() {
    int N, K;
    cin >> N >> K;
    vector<int> A(N, 0);
    for (int i = 0; i < N; ++i) {
        cin >> A[i];
    }

    vector<int> next(N, 0);
    for (int k = 0; k < K; ++k) {
        for (int i = 0; i < N; ++i) {
            for (int j = max(0, i - A[i]); j <= min(N - 1, i + A[i]); ++j) {
                next[j] += 1;
            }
        }

        for (int i = 0; i < N; ++i) {
            A[i] = next[i];
            next[i] = 0;
        }
    }

    for (int i = 0; i < N; ++i) {
        if (i > 0) {
            cout << " ";;
        }
        cout << A[i];
    }
    cout << endl;
}

int main() {
    std::cout << std::fixed << std::setprecision(15);
    Main();
    return 0;
}