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: Accepted)

"use strict";
var input = require("fs").readFileSync("/dev/stdin", "utf8");
var cin = input.split(/ |\n/),
    cid = 0;

function next() {
    return +cin[cid++];
} // number一個取得
function nextstr() {
    return cin[cid++];
} // 文字列一個取得
function nextbig() {
    return BigInt(cin[cid++]);
} // BigInteger一個取得
// 長さnの配列として取得。aは文字列フラグ
function nexts(n, a) {
    return a ? cin.slice(cid, cid += n) : cin.slice(cid, cid += n).map(a => +a);
}
// 長さnのBigInt配列として取得。
function nextsbig(n) {
    return cin.slice(cid, cid += n).map(a => BigInt(a));
}
// w個ずつを組にして長さhの配列。aは文字列フラグ。
function nextm(h, w, a) {
    var r = [],
        i = 0;
    if (a)
        for (; i < h; i++) r.push(cin.slice(cid, cid += w));
    else
        for (; i < h; i++) r.push(cin.slice(cid, cid += w).map(a => +a));
    return r;
}
// 多次元配列。v,a1,a2,a3 なら、3次元。[[値vで長さa3の配列]をa2個並べた配列]をa1個並べた配列。
function xArray(v) {
    var a = arguments,
        l = a.length,
        r = "Array(a[" + --l + "]).fill().map(x=>{return " + v + ";})";
    while (--l) r = "Array(a[" + l + "]).fill().map(x=>" + r + ")";
    return eval(r);
}

console.log(main());

function main() {
    let N = next();
    let K = next();
    let A = nexts(N);
    let t = xArray(0, N);
    let B = Array(N);
    let i, j, k, left, right;
    for (k = 0; k < K; k++) {
        left = xArray(0, N);
        right = xArray(0, N);
        for (i = 0; i < N; i++) {
            // 各Aiの電球が各点zahyoを照らしているかどうかをチェックする。
            left[Math.max(i + 1 - A[i], 1) - 1]++;
            right[Math.min(i + 1 + A[i], N) - 1]++;
        }
        //console.log({left,right});
        // 両端にすべての灯りが届いているかどうかをチェック。
        if (left[0] == N && right[N - 1] == N) {
            return xArray(N, N).join(" ");
        }
        A[0] = left[0];
        for (i = 1; i < N; i++) {
            A[i] = A[i - 1] + left[i] - right[i - 1];
        }
    }
    return A.join(" ");
}