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;
int main() {
    int N, K;
    cin >> N >> K;
    vector<int> A(N+1, 0);
    for (int i = 1; i <= N; i++) {
        cin >> A[i];
    }
    for (int k = 0; k < K; k++) {
        vector<int> v(N+2, 0);
        for (int i = 1; i <= N; i++) {
            int a = max(1, i-A[i]), b = min(N, i+A[i])+1;
            v[a]++, v[b]--;
        }
        long long S = 0;
        for (int i = 1; i <= N; i++) {
            A[i] = A[i-1] + v[i];
            S += A[i];
        }
        if (S == N*N) {
            break;
        }
    }
    for (int i = 1; i <= N; i++) {
        cout << A[i];
        if (i == N) {
            cout << endl;
        }
        else {
            cout << " ";
        }
    }
}