The AtCoder Kingdom holds a festival for $N$ days. On $M$ of these days, namely on the $A_1$-th, $A_2$-th, $\dots$, $A_M$-th days, fireworks will be launched. It is guaranteed that fireworks will be launched on the last day of the festival. (In other words, $A_M=N$ is guaranteed.)

For each $i=1,2,\dots,N$, solve the following problem.

-   How many days later from the $i$-th day will fireworks be launched for the first time on or after the $i$-th day? If fireworks are launched on the $i$-th day, it is considered to be $0$ days later.

The input is given from Standard Input in the following format:

```
$N$ $M$
$A_1$ $A_2$ $\dots$ $A_M$
```

Print $N$ lines.

The $i$-th line $(1 \le i \le N)$ should contain an integer representing the number of days from the $i$-th day until fireworks are launched for the first time on or after the $i$-th day.

-   $1 \le M \le N \le 2 \times 10^5$
-   $1 \le A_1 < A_2 < \dots < A_M = N$
-   All input values are integers.

1
0
0

The kingdom holds a festival for 3 days, and fireworks are launched on the 2-nd and 3-rd days.

• From the 1-st day, the first time fireworks are launched is the 2-nd day of the festival, which is 1 day later.
• From the 2-nd day, the first time fireworks are launched is the 2-nd day of the festival, which is 0 days later.
• From the 3-rd day, the first time fireworks are launched is the 3-rd day of the festival, which is 0 days later.