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: Time Limit Exceeded)

      program tokyoA
      implicit none

      integer(8) :: i,k,l,m,j,d,p
      real(8)::n
      integer(8),allocatable::B(:),A(:)

      read(*,*)n,k
      allocate(A(n),B(n))

      read(*,*)A(:)

      if (K >n*log(n))then
        A(:)=n
      else
      do i =1,k
        do j = 1,n
        B(j) =0
        end do
        do m =1,n
            d = A(m)
            B(m) =B(m)+1
            do l = 1,d
                if ((m+l).le.n)then
                    B(m+l) =B(m+l)+1
                endif
                if (m.gt.l)then
                    B(m-l) = B(m-l)+1
                endif
            end do
        end do
        do p = 1,n
            A(p) = B(p)
        end do

      end do
      endif

      write(*,*)A

      end program