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>

using namespace std;
typedef long long ll;
const int MAXN=1e5+10;
int n,q,tot;
ll res[MAXN],dat[MAXN],cnt[MAXN];

int Query(ll x,int r)
{
	int ret=-1,l=0;
	while(l<=r)
	{
		int mid=(l+r)>>1;
		if(dat[mid]<=x) ret=mid,l=mid+1;
		else r=mid-1;
	}
	return ret;
}
int main()
{
	scanf("%d%d",&n,&q);
	for(int i=1;i<=q;i++) scanf("%lld",&dat[i]);
	dat[0]=n;
	for(int i=1;i<=q;i++)
	{
		while(tot>=0&&dat[i]<dat[tot]) tot--;
		dat[++tot]=dat[i];
	}
	
	cnt[tot]=1;
	for(int i=tot;i>=0;i--)
	{
		ll k=dat[i],pos=Query(k,i-1);
		while(pos>=0)
		{
			cnt[pos]+=(k/dat[pos])*cnt[i];
			k=k%dat[pos];pos=Query(k,pos-1);
		}
		res[1]+=cnt[i];res[k+1]-=cnt[i];
	}
	for(int i=1;i<=n;i++)
		res[i]+=res[i-1],printf("%lld\n",res[i]);
	return 0;
}