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 main ()
  (let* ((n (read))
         (k (read))
         (b (make-array `(,(1+ n)) :initial-element 0))
         (a (make-array `(,(1+ n)) :initial-element 0))
         (stop t))
    (when (<= (1- n) k)
      (loop :for i :from 1 :to (1- n)
            :do (format t "~A " n))
      (format t "~A~%" n)
      (return-from main))
    ;; read 
    (loop :for i :from 1 :to n
          :do (setf (aref a i) (read)))
    ;;
    (loop :named main-loop
          :for _ :from 1 :to k
          :do (progn 
                (loop :for x :from 1 :to n
                      :do (let ((d (aref a x)))
                            (loop :for i :from (max 1 (- x d)) :to (min n (+ x d))
                                  :do (incf (aref b i)))))
                (loop :for i :from 1 :to n
                      :do (setf stop (and stop (= (aref a i) (aref b i))))
                      :do (setf (aref a i) (aref b i))
                      :do (setf (aref b i) 0))
                (if stop 
                    (return-from main-loop)
                    (setf stop t))))
    ;;
    (when (> n 1)
      (loop :for i :from 1 :to (1- n)
            :do (format t "~A " (aref a i))))
    (format t "~A~%" (aref a n))))
(main)