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 main()
{
	int N, K;
	cin >> N >> K;
	vector<int> A( N );
	for( int i = 0; i < N; i++ ) {
		cin >> A[i];
	}

	vector<int> b( N, N );
	vector<int> B( N );
	while( 1 ) {
		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];
		}
		K--;
		if( K <= 0 || B == b ) break;
		A = B;
		B = vector<int>( N );
	}

	for( int i = 0; i < N; i++ ) {
		if( i ) cout << " ";
		cout << B[i];
	}
	cout << endl;
}
