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: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

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

    while (K--) {
        vector<ll> inout(N+1, 0);
        for (int i = 0; i < N; i++) {
            inout[max((ll)0, i - A[i])]++;
            inout[min(N, i+A[i]+1)]--;
        }
        A[0] = inout[0];
        for (int i = 1; i < N; i++) {
            A[i] = A[i-1] + inout[i];
        }
        bool f = true;
        for (int i = 0; i < N; i++) {
            f = f && (A[i] == N);
        }
        if (f) break;
    }
    for (int i = 0; i < N; i++) {
        cout << A[i] << ' ';
    }
    cout << endl;
}