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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)


import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		// 入力
		Scanner sc = new Scanner(System.in);
		int n = Integer.parseInt(sc.next()); // 電球の個数
		int k = Integer.parseInt(sc.next()); // 操作回数
		int x[] = new int[n + 1]; // 光の強さ
		for (int i = 1; i <= n; i++) {
			x[i] = Integer.parseInt(sc.next());
		}

		// 当たっている光の数を配列にする
		int light[] = new int[n + 1];

		// 操作をk回やる
		for (int loop = 0; loop < k; loop++) {

			// 当たっている光の数を配列にする
			for (int i = 1; i <= n; i++) {
				light[i] = 0;
			}

			// 各々の電球について
			for (int i = 1; i <= n; i++) {

				// 光を当てていく
				int left = Math.max(i - x[i], 1);
				int right = Math.min(i + x[i], n);
				for (int j = left; j <= right; j++) {
					light[j]++;
				}
				// System.out.println("電球" + i + "の照らす範囲→" + left + "～" + right);
			}

			// 光の強さを更新
			System.arraycopy(light, 0, x, 0, x.length);

		}

		// 結果
		for (int i = 1; i <= n; i++) {
			System.out.print(x[i]);
			if (i < n) {
				System.out.print(" ");
			}
		}
	}

}