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;
long long b[100005];
long long a[100005];
long long t[100005];
int cur;
int main(){
	int n,q;
	cin>>n>>q;
	cur=1;
	b[1]=n;
	while(q--){
		long long x;
		cin>>x;
		while(cur&&b[cur]>=x) cur--;
		cur++;
		b[cur]=x;
	}
	t[cur]=1;
	for(int i=cur;i>=1;i--){
		long long k=b[i];
		while(true){
			if(k<=b[1]){
				break;
			}
			int j=lower_bound(b+1,b+1+cur,k)-b-1;
			t[j]+=t[i]*(k/b[j]);
			k%=b[j];
		}
		a[k]+=t[i];
	}
	for(int i=n;i>=1;i--){
		a[i]+=a[i+1];
	}
	for(int i=1;i<=n;i++) cout<<a[i]<<" ";
}