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>
     
    int main(){
       int i,j,l,m,n,k,a[200000],b[200000];
     
       scanf("%d %d",&n,&k);
       for (i=0;i<n;i++) scanf("%d",&a[i]);
       while (k>0) {
          for (i=0;i<n;i++) b[i]=0;
          for (m=i=0;i<n;i++) {
             if (a[i]==n) {
                m++;
                continue;
             }
             j=i-a[i];
             if (j<0) j=0;
             l=i+a[i];
             if (l>=n) l=n-1;
             for (;j<=l;j++) b[j]++;
          }
          for (i=0;i<n;i++) a[i]=b[i]+m;
          if (m==n) break;
          k--;
       }
       printf("%d",a[0]);
       for (i=1;i<n;i++) printf(" %d",a[i]);
       puts("");
       return 0;
    }