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: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)
func main() {
	sc.Split(bufio.ScanWords)
	N := scanInt()
	K := scanInt()
	a := make([]int, N)
	for i:= 0; i<N; i++ {
		a[i] = scanInt()
	}
	// 前の状態とあとの状態を維持する必要がある
	for i:= 0; i<K; i++ {
		//愚直にやる -> 多分無理
		b := make([]int, N)
		for j:= 0; j<N; j++ {
			light := a[j]
			// fmt.Println(a,b,light)
			for k:= j-1;(k >= 0 && k>=j-light); k-- {
				b[k] += 1
				// fmt.Println("back",k,j,"目",b,a,light)
			}
			for k:=j+1; (k<N && k<= j+light); k++ {
				b[k] += 1
				// fmt.Println("前",k,j,"目",b,a)
			}
			b[j] += 1
			// fmt.Println("")
		}
		a = b
	}
	for i:= 0; i<N; i++ {
		fmt.Print(a[i])
		fmt.Print(" ")
	}
	// 累積和？
	// x-d-0.5
	// 操作 -> 自分の光に干渉しているものをじぶんの光にする　-> graph?
	//
}
var sc = bufio.NewScanner(os.Stdin)
func scanInt () int{
	sc.Scan()
	i,_ := strconv.Atoi(sc.Text())
	return i
}