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;
#define N 300000

LL n,m,p,q[N],f[N],a[N],ans[N];

void ins(LL x,LL k){
	LL y=lower_bound(q+1,q+p+1,x)-q-1;
	if (y==0){
		ans[x]+=k;
		return;
	}
	f[y]+=k*(x/q[y]);
	ins(x%q[y],k);
}

int main(){
	scanf("%lld%lld",&n,&m);
	q[p=1]=n;
	for (LL i=1;i<=m;++i){
		LL x; scanf("%lld",&x);
		for (;p&&x<=q[p];--p);
		q[++p]=x;
	}
	f[p]=1;
	for (LL i=p;i;--i){
		ins(q[i],f[i]);
	}
	for (LL i=n;i;--i) ans[i]+=ans[i+1];
	for (LL i=1;i<=n;++i) printf("%lld\n",ans[i]);
	
	return 0;
}