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>
typedef long long i64;
const int N=100007;
int n,m,qp=0;
i64 qs[N],t[N],ans[N];
int main(){
	scanf("%d%d",&n,&m);
	qs[0]=n;
	for(int i=0;i<m;++i){
		i64 x;
		scanf("%lld",&x);
		if(x<=qs[0])qs[0]=x,qp=0;
		else{
			while(qs[qp]>=x)--qp;
			qs[++qp]=x;
		}
	}
	t[qp]=1;
	for(int i=qp;i;--i){
		i64 x=qs[i];
		while(x>=qs[0]){
			int p=std::upper_bound(qs,qs+i,x)-qs-1;
			t[p]+=x/qs[p]*t[i];
			x%=qs[p];
		}
		ans[x]+=t[i];
	}
	ans[qs[0]]+=t[0];
	for(int i=n;i;--i)ans[i-1]+=ans[i];
	for(int i=1;i<=n;++i)printf("%lld\n",ans[i]);
	return 0;
}