Problem:
Score : 1400 points

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.

Sample Input 1

5 3
6
4
11

Sample Output 1

3
3
3
2
0

After the first operation, the sequence becomes: 1,2,3,4,5,1.

After the second operation, the sequence becomes: 1,2,3,4.

After the third operation, the sequence becomes: 1,2,3,4,1,2,3,4,1,2,3.

In this sequence, integers 1,2,3,4,5 appear 3,3,3,2,0 times, respectively.

Sample Input 2

10 10
9
13
18
8
10
10
9
19
22
27

Sample Output 2

7
4
4
3
3
2
2
2
0
0

Solution in Go (1.6) (judge verdict: Accepted)

package main;import "fmt";func main(){var n,q int;var k int64;fmt.Scan(&n,&q);p:=[]int64{0,int64(n)};for i:=0;i<q;i++ {fmt.Scan(&k);j:=len(p);for k<=p[j-1] {j--};p=append(p[:j],k)};q=len(p)-1;t:=make([]int64,q+1);t[q]=1;ans:=make([]int64,n+1);for i:=q;i>0;i-- {j:=i;k=p[i];for k>p[1] {l,r:=1,j;for r-l>1 {m:=(l+r)/2;if p[m]>k {r = m} else {l = m}};j=l;t[j]+=k/p[j]*t[i];k%=p[j]};ans[k]+=t[i]};for i:=n-1;i>0;i-- {ans[i]+=ans[i+1]};for i:=1;i<n+1;i++ {fmt.Println(ans[i])}}