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<cstdio>
#define LL long long
#define maxn 100005
int n,q,r;
LL a[maxn],cnt[maxn],app[maxn],ans[maxn];
int BS(int l,int r,LL k)
{
	while(l+1<r)
	{
		int mid=(l+r)>>1;
		if(a[mid]<=k) l=mid;
		else r=mid;
	}
	return r;
}
int main()
{
	scanf("%d%d",&n,&r);
	a[q=1]=n;
	for(int i=1;i<=r;i++)
	{
		LL x;
		scanf("%lld",&x);
		while(q&&a[q]>=x) q--;
		a[++q]=x;
	}
	app[q]=1;
	for(int i=q;i;i--)
	{
		LL l=a[i];
		int p=BS(1,i-1,l);
		while(p)
		{
			app[p]+=l/a[p]*app[i];
			l%=a[p];
			p=BS(1,p-1,l);
		}
		ans[l]+=app[i];
	}
	for(int i=n;i;i--) ans[i]+=ans[i+1];
	for(int i=1;i<=n;i++) printf("%lld\n",ans[i]);
}