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)

process.stdin.resume();
process.stdin.setEncoding('utf8');
                     
var lines = [];
var reader = require('readline').createInterface({
    input: process.stdin,
    output: process.stdout
});
reader.on('line', (line) => {
    // ここで入力を処理する
    lines.push(line);
});
reader.on('close', () => {
    // ここで出力する
  var N = Number(lines[0].split(" ")[0]);
  var K = Number(lines[0].split(" ")[1]);
  var A = lines[1].split(" ");
  var B = new Array(N);

  var i=0;
  var j=0;
  var k=0;
  var l=0;

  var D =0;
  
  for(i=0;i<K;i++){
    for(j=0;j<N;j++){
      B[j]=0;
      for(k=0;k<N;k++){
        D=Math.abs(j-k);
        if(A[k]>=D){
          B[j]++;
        }
      }
    }
    for(l=0;l<N;l++){
      A[l]=B[l];
    }
  }
  console.log(A[0] + ' ' + A[1] + ' ' + A[2] + ' ' + A[3] + ' ' + A[4] );
});