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>
#define rep(i,n) for(int (i)=0;(i)<(n);++(i))
#define all(x) (x).begin(),(x).end()
#define dump(x) cout << #x << " = " << (x) << endl
using namespace std;
using ll = long long;


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

  rep(ki, k) {
    vector<int> b(n+1);
    rep(i, n) {
      int l = max(0, i - a[i]);
      int r = min(n - 1, i + a[i]);

      b[l]++;
      b[r + 1]--;
    }

    rep(i, n) b[i + 1] += b[i];
    b.pop_back();
    if (a == b) break;
    a = b;
  }

  rep(i, n) cout << a[i] << " ";
  cout << endl;
}