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)

function Main(input) {
    input = input.split("\n");
    var mem = input[0].split(" ");
    var arr = input[1].split(" ").map(Number);
    for(var p=0;p<mem[1];p++){
        var tmp = new Array(arr.length).fill(0);
        for (var i = 0; i < arr.length; i++) {
            var n = arr[i];
          //  console.log(i,n)
            var min = i - n;
            var max = i + n;
            if (min < 0) min = 0;
            if (max > arr.length-1) max = arr.length-1;
            for (var j = min; j <= max; j++) {
                tmp[j]++;
            }
          //  console.log(max,min,tmp)
        }
      //  console.log(arr)
        var flag = true;
      //  console.log(arr.length)
        for (var i = 0; i < arr.length; i++) {
            if(arr[i]!=tmp[i]) flag = false;
            arr[i] = tmp[i];
        }
     //   console.log(arr.join(" "));
        if(flag) break;
    }
    console.log(arr.join(" "));
} Main(require("fs").readFileSync("/dev/stdin", "utf8").trim());