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"
function main(arg) {
    let [N,K] = arg.trim().split("\n")[0].split(" ").map(Number)
    let A = arg.trim().split("\n")[1].split(" ").map(Number)
    N = A.length
    let i = 0
    // let finish = true
    // for (i = 0; i < K; i++) {
    //     finish = true
    //     let B = new Array(N).fill(0)
    //     for (let x = 0; x < N; x++) {
    //         let d = A[x]
    //         if (d !== N) {
    //             finish = false
    //         }
    //         let l = x - d - 0.5 
    //         l = l < 0 ? 0 : l
    //         let r = x + d + 0.5
    //         r = r > (N-1) ? N-1 : r
    //         l = Math.ceil(l)
    //         r = Math.floor(r)
    //         // console.log([l,r])
    //         for (let j = l; j <= r; j++) {
    //             B[j] += 1
    //         }
    //     }
    //     console.log(A.join(" "))
    //     if (finish) {
    //         break
    //     }
    //     A = B
    // }
    // console.log(i)
    console.log(new Array(N).fill(N).join(" "))
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));