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

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

Examples

Input

5 1
1 0 0 1 0


Output

1 2 2 1 2


Input

5 2
1 0 0 1 0


Output

3 3 4 4 3
#include <bits/stdc++.h>
using namespace std;
int n,k;
int a[200005],b[200005]; 
int main(){
	cin>>n>>k;
	for(int i=0;i<n;++i){
		cin>>a[i];
	}
	if(k>50){
		for(int i=0;i<n;++i){
			cout<<n<<' ';
		}
		cout<<'\n';
		return 0;
	}
	for(int i=0;i<k;++i){
		memset(b,0,sizeof(b));
		for(int i=0;i<n;++i){
			int l=max(0,i-a[i]);
			int r=min(n-1,i+a[i]);
			b[l]++;
			if(r+1<n){
				b[r+1]--;
			} 
		}
		for(int i=1;i<n;++i){
			b[i]+=b[i-1];
		}
		for(int i=0;i<n;++i){
			a[i]=b[i];
		}
	}
	for(int i=0;i<n;++i){
		cout<<a[i]<<' ';
	}
	cout<<'\n';
	return 0;
} 