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 N=100100;
int n,Q;
ll q[N],g[N],f[N];
void solve(ll x,ll y){
	int i=lower_bound(q,q+Q+1,y)-q-1;
	if(i<0)g[y]+=x;
	else f[i]+=x*(y/q[i]),solve(x,y%q[i]);
}

int main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin>>n>>Q;
	q[0]=n;
	for(int i=1;i<=Q;++i)
		for(cin>>q[i];i&&q[i]<=q[i-1];--i,--Q)q[i-1]=q[i];
	f[Q]=1;
	for(int i=Q;i>=0;--i)if(f[i])solve(f[i],q[i]);
	for(int i=n;i;--i)g[i]+=g[i+1];
	for(int i=1;i<=n;++i)cout<<g[i]<<'\n';
	return 0;
}