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 rep(i,k,n) for(int i=k;i<=n;i++)
#define rep2(i,k,n) for(int i=k;i>=n;i--)
using namespace std;
const int N=1e5+7;
typedef long long ll;
int n,Q,top=0;
ll q[N],f[N],yv[N];

void go(ll b,ll t){
	if(!b)return;
	int pos=lower_bound(q+1,q+top+1,b)-q-1;
	if(!pos)yv[b]+=t;
	else {
		ll k=b/q[pos];
		b-=k*q[pos];
		f[pos]+=k*t;
		
		go(b,t);
	}
}
int main(){
	scanf("%d%d",&n,&Q);
	q[++top]=n;
	rep(i,1,Q){ll x;
		scanf("%lld",&x);
		for(;x<=q[top];top--);
		q[++top]=x;
	}
	f[top]=1;
	rep2(i,top,2){
		go(q[i],f[i]);
		f[i]=0;
	}
	rep2(i,n,1)yv[i]+=yv[i+1];
	rep(i,1,q[1])
		printf("%lld\n",f[1]+yv[i]);
	rep(i,q[1]+1,n)puts("0");
	return 0;
}