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"
)

var stdInScanner = bufio.NewScanner(os.Stdin)

func nextInt() int {
	stdInScanner.Scan()
	i, _ := strconv.Atoi(stdInScanner.Text())
	return i
}

func main() {
	stdInScanner.Split(bufio.ScanWords)

	N := nextInt()
	K := nextInt()
	A := make([]int, N)
	for i := 0; i < N; i++ {
		A[i] = nextInt()
	}

	var answer []int
	var x1, x2 int
	for i := 0; i < K; i++ {
		answer = make([]int, N)
		for j := 0; j < N; j++ {
			x1 = (j + 1) - A[j] - 1
			x2 = (j + 1) + A[j] - 1
			if x1 < 0 {
				x1 = 0
			}
			if x2 >= N {
				x2 = N - 1
			}
			for k := x1; k <= x2; k++ {
				answer[k]++
			}
		}
		A = answer
	}
	w := bufio.NewWriter(os.Stdout)
	for i := 0; i < N; i++ {
		fmt.Fprint(w, answer[i], " ")
	}
	w.Flush()
}