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"
	"strings"
)

func main() {
	var n, k int64
	reader := bufio.NewReaderSize(os.Stdin, 20*1024*1024)
	line1, _, _ := reader.ReadLine()
	items := strings.Split(string(line1), " ")
	n, _ = strconv.ParseInt(items[0], 10, 32)
	k, _ = strconv.ParseInt(items[1], 10, 32)
	line2, _, _ := reader.ReadLine()
	items2 := strings.Split(string(line2), " ")
	l := len(items2)
	a := make([]float64, 0, l)
	for i := int64(0); i < n; i += 1 {
		tmp, _ := strconv.ParseInt(items2[i], 10, 32)
		a = append(a, float64(tmp))
	}
	for i := int64(0); i < k; i += 1 {
		a = f(a, int(n))
	}

	for i := int64(0); i < n; i += 1 {
		fmt.Printf("%d", int(a[i]))
		if i+1 < n {
			fmt.Print(" ")
		}
	}
}

func f(a []float64, n int) []float64 {
	result := make([]float64, 0, n)
	for x := 0; x < n; x += 1 {
		b := 0
		for j := 0; j < n; j += 1 {
			jf := float64(j)
			d := a[j]
			if (jf-d-0.5) <= float64(x) && float64(x) <= (jf+d+0.5) {
				b += 1
			}
		}
		result = append(result, float64(b))
	}
	return result
}