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 Python (3.8.2) (judge verdict: Runtime Error)

#include <iostream>
#include <iomanip>
#include <string>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <algorithm>
#include <numeric>
#include <cmath>
#include <cassert>

using namespace std;
typedef long long LL;
template <typename F, typename S> std::ostream& operator<<(ostream& os, const pair<F,S>& p) {
    os << "(" << p.first << "," << p.second << ")"; return os; }
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "["; for(const T& a: v){ os << a << ", "; } os << "]"; return os; }
template <typename K, typename V> ostream& operator<<(ostream& os, const map<K,V>& m) {
    os << "{"; for(const auto& p: m){ os << p.first <<":"<< p.second << ", "; } os << "}"; return os; }


int main(){
    LL n, k;
    cin >> n >> k;
    vector<LL> a(n);
    for(LL i = 0; i < n; ++i){
        cin >> a[i];
    }

    for(LL i = 0; i < k; ++i){
        vector<LL> diff(n+1);
        for(LL j = 0; j < n; ++j){
            LL left = max(0LL, j - a[j]);
            LL right = min(n, 1 + j + a[j]);
            diff[left] += 1;
            diff[right] -= 1;
        }
        LL cur = 0;
        for(LL i = 0; i < n; ++i){
            cur += diff[i];
            a[i] = cur;
        }
        bool flag = true;
        for(LL i = 0; i < n; ++i){
            if(a[i] != n) flag = false;
        }
        if(flag) break;
    }

    for(LL i = 0; i < n; ++i){
        if(i+1 == n){
            cout << a[i] << endl;
        }else{
            cout << a[i] << " ";
        }
    }
    return 0;
}