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: Accepted)

program main
    use,intrinsic :: iso_fortran_env
    implicit none
    integer(int64):: n,k,i,j,l,r,jj
    integer(int64), allocatable:: a(:), na(:),ims(:)
    logical:: same

    read*, n,k
    allocate(a(n), na(0:n),ims(n))
    read*, a(:)
    ! a(:) = 0
    ! a(1) = 1

    if (k >= 50) then
        a(:) = n
        print'(*(i0,1x))', a(:)
        stop
    end if

    do i=1,k
        na(:) = 0
        ims(:) = 0
        same = .true.
        do j=1,n

            l = max(j-a(j),1_8)
            r = (j+a(j)+1)
            ! print'(*(i0,1x))', j,l,r
            ims(l)=ims(l)+1
            if (r <= n) ims(r)=ims(r)-1
        end do
        ! print'(*(i0,1x))', ims(:)
        do j=1,n
            na(j) = na(j-1)+ims(j)
        end do

        do j=1,n
            if (na(j) /= a(j)) same = .false.
        end do
        if (same) exit
        a(:) = na(1:)
    end do
    ! print'(i0)', i
    print'(*(i0,1x))', na(1:)
end program main