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)

const input = require("fs").readFileSync("/dev/stdin", "utf8")
let cin = input.split(/ |\n/), cid = 0
const next = () => cin[cid++]
const nexts = (n) => cin.slice(cid, cid+=n).map(i=>parseInt(i))

const [N, K] = nexts(2)
let lamps = nexts(N)

for (let i = 0; i < K; i++) {
    let newLamps = Array(N).fill(0)
    lamps.forEach((lamp, i) => {
        for (let j = 0; j < N; j++) {
            if (i - lamp <= j && j <= i + lamp) {
                newLamps[j] += 1
            }
        }
    });
    lamps = newLamps
    if (i === N) {
        return console.log(Array(N).fill(N))
    }
}
console.log(lamps.join(' '))