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 Common Lisp (SBCL 2.0.3) (judge verdict: Time Limit Exceeded)

(defun Lamps (n k)
    (let* ((readLamps (make-array n ))
        (dousyutuLamps (make-array `(,(1+ n)) :initial-element 0))
        (stop t)
        )
 
        (dotimes (i n) 
            (setf (aref readLamps i) (read)))
 
    (loop named main-loop
          for _ below k
          do (progn 
            (loop for i below n
                do (let ((l (max 0 (- i (aref readLamps i))))
                    (r (min (- n 1) (+ i (aref readLamps i)))))
                    (incf (aref dousyutuLamps l))
                    (if (<= (1+ r) n)
                        (decf (aref dousyutuLamps (1+ r)))
                    )
                )                    
            )
            (loop for i from 1 to n
                do (incf (aref dousyutuLamps i) (aref dousyutuLamps (- i 1)))
            )
            (loop for i below n
                do (progn
                (setf stop (and stop (= (aref dousyutuLamps i) n)))
                (setf (aref readLamps i) (aref dousyutuLamps i))
                (setf (aref dousyutuLamps i) 0)
                )
            ) 
            
            (if stop
                (return-from main-loop))
        )
    )
        (loop for i below (- n 1)
            do(format t "~A "(aref readLamps i))
        )
        (format t "~A~%" (aref readLamps (- n 1))))
    
)
(Lamps (read) (read))