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: Time Limit Exceeded)

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

int main(void){
    int n,k,a[300000];
    int light[300000];
    int i,j,p;
    
    scanf("%d",&n);
    scanf("%d",&k);
    for(i = 1; i<n+1; i++){
    	scanf("%d%",&a[i]);
    }
    
    
    //light update
    
    for(p = 0; p<k; p++){
       	for(i = 1; i<n+1; i++){
    		light[i] = 0;
    	}
    	
    	for(i = 1; i<n+1; i++){
    		//printf("n = %d\n",i);
	    	for(j=0; j<a[i]+1; j++){
	    		if((i-j)>0){
	    			light[i-j] =light[i-j]+1;
	    			//printf("a[%d]= %d\n",(i-j),light[i-j]);
	    		}
	    		if((i+j)<(n+1)){
	    			light[i+j] = light[i+j]+1;
	    			//printf("a[%d]= %d\n",(i+j),light[i+j]);
	    		}
	    	}
	    	light[i] = light[i]-1;  
    		//printf("finish a[%d]= %d\n",i,light[i]);
    	}
    	for(i = 1; i<n+1; i++){
    		a[i] = light[i];
    		//printf("update a=%d",a[i]);
    	}
    	
    }
    for(i = 1; i<n+1; i++){
    	printf("%d %",light[i]);
    }


    

    
    printf("\n");
    
}