Problem:
Score : 500 points

Problem Statement

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

Sample Input 1

5 1
1 0 0 1 0

Sample Output 1

1 2 2 1 2

Initially, only Bulb 1 illuminates coordinate 1, so the intensity of Bulb 1 becomes 1 after the operation.
Similarly, the bulbs initially illuminating coordinate 2 are Bulb 1 and 2, so the intensity of Bulb 2 becomes 2.

Sample Input 2

5 2
1 0 0 1 0

Sample Output 2

3 3 4 4 3

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

# include <cstdio>
# include <cstring>
# define N 400010
int n,a[N],b[N],tree[N];
void add(int x,int y) {
	int i;
	for(i=x;i<=n;i+=i&(-i)) tree[i]+=y;
}
int query(int x) {
	int i,ans=0;
	for(i=x;i>=1;i-=i&(-i)) ans+=tree[i];
	return ans;
}
void prt() {
	for(int i=1;i<=n;i++) printf("%d ",n);
}
int main() {
	int k,i;
	scanf("%d%d",&n,&k);
	for(i=1;i<=n;i++) scanf("%d",a+i);
	if(k>40) {prt(); return 0;}
	while(k--) {
		memset(tree,0,sizeof(tree));
		for(i=1;i<=n;i++) {
			b[i]=query(n)-query(i-1);
			add(a[i]+i>n?n:a[i]+i,1);
		}
		memset(tree,0,sizeof(tree));
		for(i=n;i>=1;i--) {
			b[i]+=query(i)+1;
			add(i-a[i]<1?1:i-a[i],1);
		}
		memcpy(a,b,sizeof(b));
	}
	for(i=1;i<=n;i++) printf("%d ",a[i]);
	return 0;
}