Time limit : 2sec / Memory limit : 256MB

### 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

• $1≦N≦10^5$
• $0≦Q≦10^5$
• $1≦qi≦10^18$

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.

## CODE

ps:中途变量混乱，n m num难以分清

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