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:

$A{'}_1$ $A{'}_2$ $\ldots$ $A{'}_N$

5 1
1 0 0 1 0

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 $2$.

5 2
1 0 0 1 0

3 3 4 4 3