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>
const int N=2e5+1;
int n, k, a[N], b[N];
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) {
		memset(b+1, 0, n*sizeof(int));
		for(int i=1; i<=n; ++i) {
			++b[std::max(1, i-a[i])];
			if(i+a[i]<n) --b[i+a[i]+1];
		}
		for(int i=1; i<=n; ++i) b[i]+=b[i-1];
		if(!memcmp(a+1, b+1, n*sizeof(int))) break;
		memcpy(a+1, b+1, n*sizeof(int));
	}
	for(int i=1; i<=n; ++i) printf("%d%c", a[i], " \n"[i==n]);
	return 0;
}
