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

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

Examples

Input

5 1
1 0 0 1 0


Output

1 2 2 1 2


Input

5 2
1 0 0 1 0


Output

3 3 4 4 3
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, n) for (int i = 0; i < n; ++i)
#define rep2(i, i0, n) for (int i = i0; i < n; ++i)

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

  rep(i, k) {
    vector<ll> b(n + 1, 0);
    rep(j, n) {
      b[max(0LL, j - a[j])]++;
      b[min(n, j + a[j] + 1)]--;
    }
    a[0] = b[0];

    bool all_n = (a[0] >= n);
    rep2(j, 1, n) {
      a[j] = a[j - 1] + b[j];
      all_n &= (a[j] >= n);
    }
    if (all_n) break;
  }

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