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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

"use strict";

const main = arg => {
    const input = arg.trim().split("\n");

    const [N, K] = input[0].split(" ").map(el => parseInt(el));
    let As = input[1].split(" ").map(el => parseInt(el));
    if(K >= 50){
        console.log(new Array(N).fill(N).join(" "))
    }
    for(let k = 0; k<K; k++){
        let tmp = new Array(N+1).fill(0)
        for(let i = 0; i< N; i++){
            const d = As[i]
            if(d === 0){
                tmp[i]++
            } else {
                for(let j = i-d; j<=i+d; j++){
                    if(j < 0 || j>=N) continue
                    tmp[j]++
                }
            }
        }
        As = [...tmp]
    }
    console.log(As.join(" "))
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));