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 C# (Mono-csc 3.5.0) (judge verdict: Accepted)

using System;

namespace AtCoder {
    class Lamps {
        public static void Main(string[] args) {
            var parts = Console.ReadLine().Split(' ');
            int N = int.Parse(parts[0]);
            int K = int.Parse(parts[1]);
            int[] A = new int[N];
            parts = Console.ReadLine().Split(' ');
            for (int i = 0; i < N; i++) {
                A[i] = int.Parse(parts[i]);
            }
            for (int k = 0; k < K; k++) {
                int[] add = new int[N + 1];
                for (int i = 0; i < N; i++) {
                    int from = Math.Max(0, i - A[i]);
                    int to = Math.Min(N - 1, i + A[i]);
                    add[from]++;
                    add[to + 1]--;
                }
                int cur = 0;
                bool anySmall = false;
                for (int i = 0; i < N; i++) {
                    cur += add[i];
                    A[i] = cur;
                    if (A[i] < N) {
                        anySmall = true;
                    }
                }
                if (!anySmall) {
                    break;
                }
            }
            for (int i = 0; i < N; i++) {
                Console.Write(A[i] + " ");
            }
            Console.WriteLine();
        }
    }
}