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<cstdio>
#include<algorithm>
using namespace std;
#define MAXN 100010
#define LL long long
int n,Q,r;
LL q[MAXN],st[MAXN],a[MAXN],c[MAXN];
void Solve(LL x,LL y)
{
	int p=upper_bound(st,st+1+r,x)-st-1;
	if(!p) a[1]+=y,a[x+1]-=y;
	else c[p]+=y*(x/st[p]),Solve(x%st[p],y);
}
int main()
{
	scanf("%d%d",&n,&Q);
	if(Q==0)
	{
		for(int i=1;i<=n;i++)
			printf("1\n");
		return 0;
	}
	for(int i=1;i<=Q;i++)
		scanf("%lld",&q[i]);
	st[++r]=q[Q];
	q[0]=n;
	for(int i=Q-1;i>=0;i--)
		if(st[r]>q[i])
			st[++r]=q[i];
	for(int i=1;i<r-i+1;i++)
		swap(st[i],st[r-i+1]);
	c[r]=1;
	for(int i=r;i>1;i--)
	{
		c[i-1]+=c[i]*(st[i]/st[i-1]);
		Solve(st[i]%st[i-1],c[i]);
	}
	for(int i=1;i<=n;i++)
		a[i]+=a[i-1];
	for(int i=1;i<=st[1];i++)
		a[i]+=c[1];
	for(int i=1;i<=n;i++)
		printf("%lld\n",a[i]);
}