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;
#define RI register int
typedef long long LL;
LL read() {
	LL q=0;char ch=' ';
	while(ch<'0'||ch>'9') ch=getchar();
	while(ch>='0'&&ch<='9') q=q*10+(LL)(ch-'0'),ch=getchar();
	return q;
}
const int N=100005;
int n,Q,top;
LL st[N],num[N],ans[N];
void work(LL len,LL s) {
	int k=lower_bound(st+1,st+1+top,len)-st-1;
	if(!k) {ans[1]+=s,ans[len+1]-=s;return;}
	num[k]+=s*(len/st[k]),work(len%st[k],s);
}
int main()
{
	LL x;
	n=read(),Q=read(),st[++top]=n;
	while(Q--) {
		x=read();
		while(top&&st[top]>x) --top;
		st[++top]=x;
	}
	num[top]=1;
	for(RI i=top;i>=1;--i) work(st[i],num[i]);
	for(RI i=1;i<=n;++i) ans[i]+=ans[i-1];
	for(RI i=1;i<=n;++i) printf("%lld\n",ans[i]);
	return 0;
}