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 light
  implicit none
  integer :: n, k, i, j
  integer,allocatable :: a(:), a2(:)

  read(*,*) n, k

  if ( k>=n ) then
     read(*,*)
     do i = 1, n
        write(*,'(200000(i0,x))',advance='no') n
     end do
     stop
  end if
  
  allocate(a(n),a2(n))
  read(*,*) a
  a2 = 0
  do i = 1, k
     do j = 1, n
        a2(max(1,j-a(j)):min(j+a(j),n))= a2(max(1,j-a(j)):min(j+a(j),n)) + 1
     end do
     a = a2
     a2 = 0
     if (minval(a)==n) then
        exit
     end if
  end do
  write(*,'(200000(i0,x))') a
  deallocate(a,a2)
  stop
end program light