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;
typedef long long ll;
#define int ll
int32_t main()
{
	int n,k,l,r;
	cin>>n>>k;
	int a[n];
	int b[n];
	for(auto &i:a)cin>>i;
	int t[n];
	bool eq;
	for(int i=0;i<n;i++)t[i]=n;
	while(k--)
	{
		eq=1;
		for(int i=0;i<n;i++)b[i]=0;
		for(int i=0;i<n;i++)
		{
			l=max(0LL,i-a[i]);
			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++)
		{if(a[i]!=t[i]){eq=0;break;}}
		if(eq)break;
	}
	for(auto i:a)cout<<i<<" ";
}