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 N (100009)
#define ll long long
using namespace std;
ll n,q,x,a[N],c,A[N],f[N];
int main()
{
	cin>>n>>q;
	a[++c]=n;
	for (ll i=1; i<=q; ++i)
	{
		cin>>x;
		while (c && x<=a[c]) --c;
		a[++c]=x;
	}
	f[c]=1;
	for (ll i=c; i; --i)
	{
		ll k=a[i];
		while (k>a[1])
		{
			ll t=lower_bound(a+1,a+c+1,k)-a-1;
			f[t]+=f[i]*(k/a[t]);
			k%=a[t];
		}
		A[k]+=f[i];
	}
	for (ll i=n; i; --i) A[i]+=A[i+1];
	for (ll i=1; i<=n; ++i) cout<<A[i]<<endl;
}