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';
function Main(stdin){
  const input = stdin.trim().split(/\r?\n/g);
  const N_K = input[0].split(' ').map(str => Number(str));
  const N = N_K[0], K = N_K[1];
  let A = input[1].split(' ').map(str => Number(str));
  let max = 0, min = 0;
  let result = new Array(N);

  for(let i = 0; i < K; i++){
      result.fill(0);
      for(let j = 0; j < N; j++){
          for(let k = 0; k < N; k++){
            if(A[k] >= Math.abs(j-k)){
                result[j] += 1;
            }
          }
      }
      A = result.slice(0);
  }
  console.log(result.join(' '));
}

// 固定
Main(require("fs").readFileSync("/dev/stdin", "utf8"));