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: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

#define rep(i,k,n) for(int (i)=(k);(i)<(n);(i)++)
#define max(a,b) (a)>(b)?(a):(b)
#define min(a,b) (a)<(b)?(a):(b)
#define abs(a) (a)>0 ?(a):-(a)
#define llong long long

int main(){
	int N,K; scanf("%d %d",&N,&K);
	int a[N];
	rep(i,0,N) scanf("%d",&a[i]);
	int lamp[N],plus[N];
	rep(i,0,N) lamp[i]=0;
	rep(i,0,N){
		int min = max(0,i-a[i]);
		int max = min(N,i+a[i]+1);
		rep(j,min,max){
			lamp[j]++;
		}
	}
	
	rep(k,0,K){
		rep(i,0,N) plus[i]=0;
		rep(i,0,N){
			int d = lamp[i]-a[i];	// 広がる範囲
			int min = max(0,i-lamp[i]);
			rep(j,min,i-a[i]) plus[j]++;
			int max = min(N,i+lamp[i]+1);
			rep(j,i+a[i]+1,max) plus[j]++;
		}
		rep(i,0,N) a[i] = lamp[i];
		rep(i,0,N) lamp[i]+=plus[i];
	}
	
	rep(i,0,N) printf("%d ",a[i]);
		
	return 0;
}