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: Wrong Answer)

#include <bits/stdc++.h>
#include <string.h>
using namespace std;
using ll=long long;
using P = pair<int,int>;
#define rep(i,n) for(int i=0;i<(int)(n);i++)
const int INF =1001001001;

int main()
{
    int n, k;
    cin >> n >> k;
    vector<ll> a(n);
    rep(i,n) cin >> a[i];
    k = min(k, (int)log(n));
    rep(i, k)
    {
        vector<ll> memo(n);
        rep(j,n)
        {
            int l = j - a[j];
            int r = j + a[j];
            if(l < 0) l = 0;
            if(r >= n) r = n -1;

            rep(x, r-l+1) memo[x + l]++;
        }
        a = memo;
    }

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