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 s64;
#define rep(i,l,r) for(int i=l;i<=r;++i)
#define per(i,r,l) for(int i=r;i>=l;--i)
const int N=1e5+5;
s64 w[N],w0[N],q[N];

int main()
{
	//freopen("1.in","r",stdin);
	int n,m;
	cin>>n>>m;
	int top=0;q[0]=n;
	rep(i,1,m)
	{
		s64 qi;
		scanf("%lld",&qi);
		while(top>=0&&q[top]>=qi)--top;
		q[++top]=qi;
	}
	w[top]=1;
	per(i,top,0)
	{
		s64 l=q[i];
		int j=i;
		while(l>q[0])
		{
			j=lower_bound(q,q+j,l)-q-1;
			w[j]+=l/q[j]*w[i];
			l%=q[j];
		}
		w0[l]+=w[i];
	}
	per(i,q[0],1)w0[i]+=w0[i+1];
	rep(i,1,n)printf("%lld\n",w0[i]);
}