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 maxn 100010
#define ms(x,y) memset(x,y,sizeof x)
#define inf 0x3f3f3f3f
#define fir first
#define sec second
#define lb(x) (x&(-x))
const int mod=1e9+7;
using namespace std;
typedef long long ll;
typedef pair<int,int> pi;
int n,q,top;ll stk[maxn],t[maxn],a[maxn],s[maxn];
int main(){
	scanf("%d%d",&n,&q);
	stk[++top]=n;ll x;
	for(int i=1;i<=q;i++){
		scanf("%lld",&x);
		while(top&&stk[top]>=x)top--;
		stk[++top]=x;
	}
	q=top;
	for(int i=1;i<=q;i++)a[i]=stk[i];
	t[q]=1;
	for(int i=q;i;i--){
		ll k=a[i];int p=lower_bound(a+1,a+i,k)-a-1;
		while(p){
			t[p]+=k/a[p]*t[i];
			k%=a[p];p=lower_bound(a+1,a+p,k)-a-1;
		}
		s[1]+=t[i];s[k+1]-=t[i];
	}
	ll res=0;
	for(int i=1;i<=n;i++){
		res+=s[i];printf("%lld\n",res);
	}
	return 0;
}