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 <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <cmath>
#include <map>
#include <string>
#define int long long
#define REP(i,n) for(int i=0; i<n; i++)
#define pb push_back
#define mp make_pair
#define Pii pair< int, int > 
#define Pid pair< int, double > 
#define Pdd pair< double, double > 
#define MOD 1000000007
#define EPS 0.00000001
using namespace std;

using Graph = vector<vector<Pii > >;

vector<bool> seen;
vector<int> color;
bool ok = true;

signed main() {
    int n,k;
    cin >> n >> k;
    vector<int> a;
    REP(i,n) {
        int at;
        cin >> at;
        a.push_back(at);
    }
    while (k > 0) {
        if (*min_element(a.begin(), a.end()) != n) {
            vector<int> b(n+1);
            REP(i,n) {
                b[max(0LL,i-a[i])] ++;
                b[min(n,i+a[i]+1)] --;
            }
            a[0] = b[0];
            REP(i,n-1) {
                int j=i+1;
                b[j] += b[j-1];
                a[j] = b[j];
            }
        } else {
            break;
        }
        k--;
    }
    REP(i,n) {
        cout << a[i] << " ";
    }
    cout << "\n";
    return 0;
}