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;

using ll=long long;

int main(){
  int n,q;cin>>n>>q;
  vector<ll> v;
  v.push_back(n);
  while(q--){
    ll a;cin>>a;
    while(v.size()&&v.back()>=a)v.pop_back();
    v.push_back(a);
  }
  int L=v.size();
  vector<ll> t(L,0),ans(n+1,0);
  t[L-1]=1;
  for(int i=L-1;i>=0;i--){
    ll k=v[i];
    int j=i;
    while(j){
      if(v[0]>k)break;
      int l=0,r=j;
      while(r-l>1){
        int mid=(r+l)>>1;
        (v[mid]>k?r:l)=mid;
      }
      t[l]+=t[i]*(k/v[l]);
      k%=v[l];
      j=l;
    }
    ans[0]+=t[i];
    ans[k]-=t[i];
  }
  for(int i=0;i<n;i++){
    cout<<ans[i]<<endl;
    ans[i+1]+=ans[i];
  }
}