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;
using ll=long long;
int n,k,a[1<<18],d[1<<18],oa[1<<18];
int main(){
	scanf("%d%d",&n,&k);
	for(int i=1;i<=n;i++)scanf("%d",a+i);
	for(int i=1;i<=k;i++){
		memcpy(oa,a,sizeof a);
		memset(d,0,sizeof d);
		for(int j=1;j<=n;j++)d[max(j-a[j],1)]++,d[min(j+a[j],n)+1]--;
		for(int j=1;j<=n;j++)a[j]=a[j-1]+d[j];
		if(!memcmp(a,oa,sizeof a))break;
	}
	for(int i=1;i<=n;i++)printf("%d%c",a[i]," \n"[i==n]);
	return 0;
}