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,x,y) for (int i=(x);i<=(y);i++)
#define ll long long

using namespace std;

const int N=1e5+100;
int n,q,m;
ll l[N],tag[N],c[N];

void solve(ll x,ll v){
	if (!x) return;
	int p=upper_bound(l+1,l+1+m,x)-l-1;
	if (!p){c[1]+=v,c[x+1]-=v; return;}
	tag[p]+=(x/l[p])*v;
	solve(x%l[p],v);
}

int main(){
	scanf("%d%d",&n,&q); l[m=1]=n;
	rep (i,1,q){
		ll x; scanf("%lld",&x);
		while (m&&l[m]>=x) m--; l[++m]=x;
	}
	tag[m]=1;
	for (int i=m;i>1;i--){
		tag[i-1]+=tag[i]*(l[i]/l[i-1]);
		solve(l[i]%l[i-1],tag[i]);
	}
	c[1]+=tag[1]; c[l[1]+1]-=tag[1];
	rep (i,1,n) c[i]+=c[i-1], printf("%lld ",c[i]);
	return 0;
}