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;
#define rep(i, a, b) for (int i = a; i < (int)(b); i++)
#define all(v) v.begin(), v.end()
const int MOD = 1e9 + 7;
const int INF = 1e9;
//'A' = 65, 'Z' = 90, 'a' = 97, 'z' = 122

int main() {
    int n, k;
    cin >> n >> k;
    int a[n];
    rep(i, 0, n) cin >> a[i];
    int cnt[n + 1] = {};
    k = min(k, 50);
    while (k--) {
        rep(i, 0, n) {
            int s = max(0, i - a[i]);
            int e = min(n - 1, i + a[i]);
            cnt[s]++;
            cnt[e + 1]--;
        }
        rep(i, 0, n - 1) cnt[i + 1] += cnt[i];
        rep(i, 0, n) a[i] = cnt[i];
        rep(i, 0, n + 1) cnt[i] = 0;
    }
    rep(i, 0, n) cout << a[i] << " ";
    cout << endl;
    return 0;
}