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: Time Limit Exceeded)

"use strict";

const main = arg => {
    const inputList = arg.trim().split("\n");
    // 回答を記述
    const N = parseInt(inputList[0].split(" ")[0]);
    const K = parseInt(inputList[0].split(" ")[1]);
    let ALightList = inputList[1].split(" ").map(ele => parseInt(ele));

    for (let i = 0; i < K; i++) {
        const changeSumList = Array(ALightList.length).fill(0);
        for (let j = 0; j < ALightList.length; j++) {
            const minus = (j - ALightList[j]) < 0 ? 0 : j - ALightList[j];
            const plus = j + ALightList[j] > N ? N : j + ALightList[j];
            for (let k = minus; k <= plus; k++) {
                if (changeSumList[k] < N) {
                    changeSumList[k]++;
                }
            }
        }
        ALightList = changeSumList;
    }
    console.log(ALightList.join(" "))
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));