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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::{
   fastout, input,
   marker::{Bytes, Chars, Isize1, Usize1},
};

#[fastout]
fn main() {
   input! {
      n:usize,k:usize,
      mut a:[isize;n]
   }
   let mut v = vec![0; n];
   for _ in 0..k {
      for i in 0..n {
         v[if a[i] as usize > i {
            0
         } else {
            i - a[i] as usize
         }] += 1;

         if a[i] as usize + i + 1 < n {
            v[i + a[i] as usize + 1] -= 1;
         }
      }
      for i in 1..n {
         v[i] += v[i - 1];
      }
      if a == v {
         break;
      }
      a = v;
      v = vec![0; n];
   }
   for i in a {
      print!("{} ", i);
   }
   println!("");
}