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=1e5+5;
int n,m,i;
ll q[N],ans[N];
map<ll,ll>mp;
int main(){
	scanf("%lld%d",q,&m);
	for(i=1;i<=m;++i)scanf("%lld",q+i);mp[q[m]]=1;
	for(i=m-1;i>=0;--i)for(auto it=--mp.end();it->first>q[i];mp.erase(it--)){
		ll x=it->first/q[i],y=it->first-q[i]*x;
		mp[q[i]]+=x*it->second;if(y)mp[y]+=it->second;
	}
	for(i=*q;i;--i)ans[i]=ans[i+1]+mp[i];
	for(i=1;i<=*q;++i)printf("%lld\n",ans[i]);
	return 0;
}