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>
#define rep(i, a, b) for(int i = a; i < b; i++)
#define Rep(i, a, b) for(int i = a; i <= b; i++)
#define repr(i, a, b) for(int i = a; i >= b; i--)
#define _GLIBCXX_DEBUG
#define Vl vector<ll>
#define Vs vector<string>
#define Vp vector<pair<ll, ll>>
#define ld long double
using ll = long long;
#define ALL(v) (v).begin(),(v).end()
#define endl "\n"
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define co(x) cout << x << endl
#define coel cout << endl
#define pb push_back
#define sz(v) ((ll)(v).size())
using namespace std;  
const double pi = acos(-1.0);
const ll MOD = 1e9 + 7;
const ll INF = 1LL << 60;
#define pp pair<ll, pair<ll, ll>> 
#define fi first
#define se second

void print(Vl vec){
    rep(i, 0, sz(vec)){
        if(i) cout << " ";
        cout << vec[i];
    }
    coel;
}

////////////////////////////////////////////////////////

// デバッグを消し忘れるな！！！

int main() {
    ll n, k; cin >> n >> k;
    Vl a(n+2); 
    Rep(i, 1, n) cin >> a[i];

    // k >= n のときは全部nになる
    if(k >= n){
        rep(i, 0, n){
            if(i) cout << " ";
            cout << n;
        }
        coel;
        return 0;
    }

    // // 愚直にやったら計算量O(n*k) (n*k >= 10^10)
    Vl d(n+2, 0);
    Vl e;
    do{
        e = a;
        rep(i, 0, n+2) d[i] = 0;
        Rep(i, 1, n){
            if(a[i] == 0){continue;}
            ll l = max(1LL, i-a[i]), r = min(n, i+a[i]);
            d[l]++; d[r+1]--;
        }
        Rep(i, 2, n){
            d[i] += d[i-1];
        }
        Rep(i, 1, n) if(a[i] == 0) d[i]++;    
        a = d;
        k--;
    }while(k != 0 && e != a);

    Rep(i, 1, n) cout << d[i] << " ";
    coel;


    return 0;
}