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;

template <typename _Tp> inline _Tp read(_Tp&x){
	char c11=getchar();x=0;while(!isdigit(c11))c11=getchar();
	while(isdigit(c11))x=x*10+c11-'0',c11=getchar();return x;
}

const int N=101000;
ll k[N],a[N],dx[N],n;
int q,top;

int main(){
	read(n),read(q);
	a[top=1]=n;
	for(int i=1;i<=q;++i){
		ll x;read(x);
		while(top&&a[top]>=x)--top;
		a[++top]=x;
	}k[top]=1;
	for(int i=top,id;i;--i){
		ll L=a[i],l;
		while(L>a[1]){
			id=upper_bound(a+1,a+i,L)-a-1;
			l=a[id],k[id]+=k[i]*(L/l),L%=l;
		}dx[L]+=k[i];
	}
	for(int i=n;i;--i)dx[i]+=dx[i+1];
	for(int i=1;i<=n;++i)printf("%lld\n",dx[i]);
	return 0;
}