Problem: 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.

Examples

Input

5 3
6
4
11


Output

3
3
3
2
0


Input

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


Output

7
4
4
3
3
2
2
2
0
0

Solution (in CPP):

Solution:
#include<bits/stdc++.h>

typedef long long LL;
using namespace std;

const int MX=100005;
int n,Q;
LL a[MX],dt[MX],t[MX],x,cur,c;

int main(){
	cin>>n>>Q,a[++c]=n;
	for(int i=1;i<=Q;i++){cin>>x;while(c&&x<=a[c])--c;a[++c]=x;}
	t[c]=1;
	for(int i=c;i;i--){
		LL tmp=a[i],it=upper_bound(a,a+i,tmp)-a-1;
		for(;it;it=upper_bound(a,a+it,tmp)-a-1)t[it]+=(tmp/a[it])*t[i],tmp%=a[it];
		dt[1]+=t[i],dt[tmp+1]-=t[i];
	}
	for(int i=1;i<=n;i++)cout<<(cur+=dt[i])<<endl;
	return 0;
}