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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

// 1行読み込み
func nextLine() string {
	sc.Scan()
	return sc.Text()
}

// 読み込みをint型へキャスト
func nextInt() int {
	sc.Scan()
	num, err := strconv.Atoi(sc.Text())
	if(err != nil) {
		panic(err)
	}
	return num
}

func main() {
	// scannerの挙動を改行区切り → 空白区切りに変更
	sc.Split(bufio.ScanWords)
	n, k := nextInt(), nextInt()
	// shine := make([]int, n, n)
	shine := make(map[int]int, n)
	
	for i := 0; i < n; i++ {
		shine[i] = nextInt()
	}
	
	for m := 0; m < k; m++ {
		next_list := make(map[int]int, n)
		for i, num := range shine {
			next_list[i] += 1
			if num > 0 {
				for l := 1; l <= num; l++ {
					if i - l >= 0 {
						next_list[i - l] += 1
					}
					if i + l < len(next_list) {
						next_list[i + l] += 1
					}
				}
			}
		}
		shine = next_list
	}

	for o := 0; o < n; o++ {
		if o == n - 1 {
			fmt.Print(strconv.Itoa(shine[o]) + "\n")
		} else {
			fmt.Print(strconv.Itoa(shine[o]) + " ")
		}
	}
}