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: Runtime Error)

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

int* light_change(int* A,int N,int K){
    int* B=(int*)malloc(sizeof(int));
    
    int i,j,k;
    for(k=0;k<K;k++){
        for(i=0;i<N;i++){
            B[i]=0;
        }
       for(i=0;i<N;i++){
           for(j=(i-A[i]>=0? i-A[i]:0); j<(i+A[i]+1<=N ? i+A[i]+1: N); j++){
            B[j]++;
        }
    }
    for(i=0;i<N;i++){
        A[i]=B[i];
    }
    }
    free(B);
    return A;
}


int main(void){
    // Your code here!
    int N,K;
    scanf("%d %d",&N,&K);

    int* A=(int*)malloc(sizeof(int)*N);
    
    int i=0;
    for(i=0; i<N;i++){
        scanf("%d",&(A[i]));
    }
    light_change(A,N,K);
    
    
    for(i=0;i<N;i++){
        printf("%d ",A[i]);
    }
    return 0;
}