Problem Statement

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.

Input

The input is given from Standard Input in the following format:
N M
$A_1 A_2 \dots A_M$

Output

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.

Constraints

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

Sample Input 1

3 2
2 3

Sample Output 1

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.

Sample Input 2

8 5
1 3 4 7 8

Sample Output 2

0
1
0
0
2
1
0
0

见题面 Input 部分

见题面 Output 部分