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>
#include<algorithm>
#include<iostream>
#define N 200005
using namespace std;
int n,q,m;
long long Q,V[N],ans[N],a[N];
void CL(long long x,long long v)
{
	int P;
	P=upper_bound(a+1,a+m+1,x)-a-1;
	if (!P)
	{
		ans[1]+=v;
		ans[x+1]-=v;
		return;
	}
	V[P]+=v*(x/a[P]);
	CL(x%a[P],v);
}
int main()
{
	scanf("%d%d",&n,&q);
	m++;
	a[m]=n;
	for (int i=1;i<=q;i++)
	{
		scanf("%lld",&Q);
		while (Q<=a[m])
			m--;
		a[++m]=Q;
	}
	V[m]=1;
	for (int i=m;i>1;i--)
	{
		V[i-1]+=V[i]*(a[i]/a[i-1]);
		CL(a[i]%a[i-1],V[i]);
	}
	ans[0]=0;
	ans[1]+=V[1];
	ans[a[1]+1]-=V[1];
	for (int i=1;i<=n;i++)
	{
		ans[i]+=ans[i-1];
		printf("%lld\n",ans[i]);
	}
	return 0;
}