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) {
 
	// 1行目がinput[0], 2行目がinput[1], …に入る
    input = input.split("\n");
  
    let N = parseInt(input[0].split(" ")[0]);
    let K = parseInt(input[0].split(" ")[1]);
    
    let d = input[1].split(" ").map(v => parseInt(v));
    
    for (let i = 1; i <= K; i++) d = make_d(d);
    
    console.log(d.join(" "));
}

function make_d(d){
    
    let b_i = (new Array(d.length)).fill(0);
        
    d.forEach((value, index) => {
        
        let d_min = index - value >= 0 ? index - value : 0;
        let d_max = index + value + 1;
        
        b_i[d_min] += 1;
        if (d_max < b_i.length) b_i[d_max] -= 1;
        
    });
    
    for(let i = 0; i < b_i.length; i++) if(0 < i) b_i[i] += b_i[i - 1];
    
    return b_i;
    
}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));