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>
const int MaxN=100010,MaxQ=100010;
long long q[MaxN],c[MaxN],f[MaxQ];
long long go(long long&x,int&r){
	int l=r-1,mid;
	while(l>1&&q[l]>=x)l=l*2-r;
	for(l<1?l=1:1;r-l>1;)
		q[mid=l+r>>1]<x?l=mid:r=mid;
	long long t=x/q[l];
	x%=q[l];r=l;
	return t;
}
int main(){
	int N,Q,n=1;
	long long x;
	scanf("%d%d",&N,&Q);
	q[1]=N;
	while(Q--){
		scanf("%lld",&x);
		while(n&&q[n]>=x)--n;
		q[++n]=x;
	}
	f[n]=1;
	for(int i=n;i;i--){
		x=q[i];
		int j=i;
		while(x>q[1]){
			long long t=go(x,j);
			f[j]+=t*f[i];
		}
		c[x]+=f[i];
	}
	for(int i=N;--i;)c[i]+=c[i+1];
	for(int i=1;i<=N;i++)printf("%lld\n",c[i]);
}