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 Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

program main
    implicit none
    integer n,k
    integer i,j,l, tau, sum
    integer, allocatable, dimension(:) :: a, b

    read(*,*) n, k
    allocate(a(n))
    allocate(b(n))
    read(*,*) a

    sum = 0
    do i = 1,n
        sum = sum + a(i)
    end do

    if (sum /= 0) then
        tau = 2*int(log(real(n))) + 10

        if(k > tau) then
            a = n
        else 
            do l = 1,k

                b = 0
                do i = 1,n
                    do j = i-a(i), i+a(i)
                        if(j >= 1 .and. j <= n) then
                            b(j) = b(j) + 1
                        end if
                    end do
                end do

                do i = 1,n
                    a(i) = b(i)
                end do

            end do
        end if

    else
        a = 0
    end if

    write(*,*) a

end program