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;
use std::io::{stdout, Write};
use std::cmp;

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<usize> = A.trim().split_whitespace().map(|e| e.parse::<usize>().unwrap()).collect();
    let mut n :usize = vecS[0].parse().unwrap();
    let mut k :usize = vecS[1].parse().unwrap();
    let mut tempvec :Vec<usize> = Vec::new();
    let mut left : usize = 0;
    let mut right : usize = 0;
    tempvec = vec![0; n];
    for i in 0..k{
        for j in 0..n{
            left = cmp::max(0 ,j as isize- vecA[j] as isize) as usize;
            right = cmp::min(n-1, j + vecA[j]);
            for k in left..=right{
                tempvec[k] += 1;
            }
        }
        vecA = tempvec;
        tempvec = vec![0; n];
    }
    let out = stdout();
    let mut out = out.lock();
    for i in 0..n-1{
        write!(out, "{} ",vecA[i]).unwrap();
    }
    write!(out, "{}\n",vecA[n-1]).unwrap();
}