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;
const int N=1e5+5;
inline long long read(){
	register long long x=0;
	register char ch=getchar();
	while(ch<'0'||ch>'9')	ch=getchar();
	while(ch>='0'&&ch<='9')	x=x*10+(ch^48),ch=getchar();
	return x;
}
int n,q,top;
long long b[N],st[N],res[N];
void solve(long long x,long long val){
	if(x<=n){
		b[x]+=val;
		return ;
	}
	int k=lower_bound(st+1,st+top+1,x)-st-1;
	res[k]+=val*(x/st[k]);
	solve(x%st[k],val);
}
int main(){
	st[top=1]=n=read(),q=read();
	while(q--){
		long long p=read();
		while(top&&st[top]>=p)	--top;
		st[++top]=p;
	}
	res[top]=1,q=n,n=st[1];
	for(int i=top;i;i--)	solve(st[i],res[i]);
	for(int i=q;i;i--)	b[i]+=b[i+1];
	for(int i=1;i<=q;i++)	printf("%lld\n",b[i]);
	return 0;
}