Problem Statement

Snuke got an integer sequence from his mother, as a birthday present. The sequence has $N$ elements, and the $i$-th of them is $i$. Snuke performs the following $Q$ operations on this sequence. The $i$-th operation, described by a parameter $q_i$, is as follows:

• Take the first $q_i$ elements from the sequence obtained by concatenating infinitely many copy of the current sequence, then replace the current sequence with those $q_i$ elements.

After these $Q$ operations, find how many times each of the integers $1$ through $N$ appears in the final sequence.

Constraints

• $1 ≦ N ≦ 10^5$
• $0 ≦ Q ≦ 10^5$
• $1 ≦ q_i ≦ 10^{18}$
• All input values are integers.

Input

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

N Q
q_1
:
q_Q

Output

Print $N$ lines. The $i$-th line $(1 ≦ i ≦ N)$ should contain the number of times integer $i$ appears in the final sequence after the $Q$ operations.