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: Time Limit Exceeded)

use std::io;

fn main() {
    let mut S = String::new();
    let mut A = String::new();
    io::stdin().read_line(&mut S);
    io::stdin().read_line(&mut A);
    let mut vecS :Vec<&str> = S.trim().split_whitespace().collect();
    let mut vecA :Vec<&str> = A.trim().split_whitespace().collect();
    let mut n :usize = vecS[0].parse().unwrap();
    let mut k :usize = vecS[1].parse().unwrap();
    let mut count :usize = 0;
    let mut vec :Vec<usize> = Vec::new();
    for i in 0..n{
        vec.push(vecA[i].parse::<usize>().unwrap());
    }
    let mut tempvec :Vec<usize> = Vec::new();
    tempvec = vec.clone();
    for i in 0..k{
        for j in 0..n{
            count = 0;
            for k in 0..n{
                if (k*2) as i64 - (vec[k]*2) as i64 - 1 < ((2*j) as i64) {
                    if (k*2 + vec[k]*2 + 1) > j*2 {
                        count = count + 1;
                    }
                }
            }
            tempvec[j] = count;
        }
        vec = tempvec.clone();
    }
    let mut answer = String::new();
    for i in 0..n{
        answer = format!("{} {}",answer,vec[i].to_string())
    }
    println!("{}",answer.trim()); 
}