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)

#[allow(unused_imports)]
use proconio::{fastout, input, marker::*};

#[fastout]
fn main() {
   input! {
      n: usize,
      k: usize,
      mut a: [usize; n],
   }
   if n <= k {
      for _ in 0..n {
         print!("{} ", n);
      }
      println!("");
      return;
   }

   for _ in 0..k {
      let mut s = vec![0i64; n + 1];
      for i in 0..n {
         let l = if i > a[i] { i - a[i] } else { 0 };
         let r = if i + a[i] < n { i + a[i] + 1 } else { n };
         s[l] += 1;
         s[r] -= 1;
      }
      let mut flag = true;
      for i in 0..n {
         if i != 0 {
            s[i] += s[i - 1];
         }
         a[i] = s[i] as usize;
         if a[i] != n {
            flag = false;
         }
      }
      if flag {
         break;
      }
   }
   for i in 0..n {
      print!("{} ", a[i]);
   }
   println!("");
}