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;
using lint = long long;
using P = pair<int, int>;
using vec = vector<int>;
using mat = vector<vector<int>>;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define all(v) v.begin(), v.end()
#define endl "\n"

constexpr int MOD = 1000000007;
const int INF = 1 << 30;

int main() {
    int n, k;
    cin >> n >> k;
    vec a(n);
    rep(i, n) cin >> a[i];

    rep(_, min(k, 1000)) {
        vec im(n+1);
        rep(i, n) {
            im[max(0, i-a[i])]++;
            im[min(n, i+a[i]+1)]--;
        }
        rep(i, n) im[i+1] += im[i];
        rep(i, n) a[i] = im[i];
    }

    rep(i, n) {
        if (i != 0) cout << " ";
        cout << a[i];
    }
    cout << endl;
    return 0;
}