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>
#define ll long long
#define inf(x) (ll)(1e##x)
using namespace std;
template<typename tn> void read(tn &a){
	tn x=0,f=1; char c=' ';
	for(;!isdigit(c);c=getchar()) if(c=='-') f=-1;
	for(;isdigit(c);c=getchar()) x=x*10+c-'0';
	a=x*f;
}
int n,Q,top;
ll st[101000],p[101000],h[101000];
int main(){
	read(n);read(Q);
	st[++top]=n;
	for(int i=1;i<=Q;i++){
		ll x;read(x);
		while(top>0&&st[top]>=x) top--;
		st[++top]=x;
	}
	p[top]=1;
	for(int i=top;i>1;i--){
		ll now=st[i];
		int k=lower_bound(st+1,st+top+1,now)-st-1;
		while(k){
			p[k]+=(now/st[k])*p[i];
			now%=st[k];
			k=lower_bound(st+1,st+top+1,now)-st-1;
		}
		if(now) h[now]+=p[i];
	}
	h[st[1]]+=p[1];
	for(int i=st[1]-1;i;i--) h[i]+=h[i+1];
	for(int i=1;i<=n;i++) cout<<h[i]<<'\n';
	return 0;
}