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: Runtime Error)

#include<cmath>
#include <bits/stdc++.h>
using ll = long long;
using namespace std;
stack<int> st;
queue<int> qu;
queue<pair<int,int> > qu2;
priority_queue<int> pq;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
#define rep2(i,n) for(int i=1; i<=(int)(n); i++)
#define mins(x,y) x=min(x,y)
#define maxs(x,y) x=max(x,y)
typedef set<int> set_t;
typedef set<string> set_g;
typedef complex<double> xy_t;
static const int NIL = -1;
static const int INF = 1000000007;
#define mp make_pair
#define sz(x) int(x.sise())
#define mod 1000000007
#define reps(i,s,n) for(int i = s; i < n; i++)
#define Rreps(i,n,e) for(int i = n - 1; i >= e; --i)
#define Rrep(i,n) Rreps(i,n,0)
deque<int> deq;
#define fi first
#define se second
//const ll MOD = 998244353;
const ll MOD = (1e+9) + 7;
typedef pair<int, int> P;
priority_queue<pair<ll,int>> V;
int a[200005];
int main(){
    int n,k;
    cin >> n>> k;
    rep(i,n){
        cin >> a[i];
        V.push(mp(-(i-a[i]),1));
        V.push(mp(-(i+a[i]+1),-1));
    }
    rep(i,k){
        int kk=0;
        int temp=0;
        /*
        priority_queue<pair<ll,int>> V2=V;
        while(!V2.empty()){
            pair<ll,int> U2=V2.top();
            V2.pop();
            cerr<<U2.fi<<' '<<U2.se<<endl;
        }
        */
        while(!V.empty()){
            pair<ll,int> U=V.top();
            V.pop();
            if(-(U.fi)>kk){
                while(kk<-(U.fi)){
                    a[kk]=temp;
                    kk++;
                    //cerr<<kk<<' '<<temp<<endl;
                }
            }
            temp+=U.se;
        }
        
        rep(j,n){
            V.push(mp(-(j-a[j]),1));
            V.push(mp(-(j+a[j]+1),-1));
        }
    }
    rep(j,n){
        cout<<a[j]<<' ';
    }
    cout<<endl;
    return 0;
}