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 int64 = long long;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector< int64 > st{N};
  for(int i = 0; i < Q; i++) {
    int64 x;
    cin >> x;
    while(st.size() && st.back() >= x) st.pop_back();
    st.emplace_back(x);
  }
  map< int64, int64 > rot;
  rot[st.back()] = 1;
  for(int i = (int) st.size() - 2; i >= 0; i--) {
    while(prev(end(rot))->first > st[i]) {
      auto it = *prev(end(rot));
      rot.erase(prev(end(rot)));
      if(it.first / st[i] > 0) rot[st[i]] += (it.first / st[i]) * it.second;
      if(it.first % st[i] > 0) rot[it.first % st[i]] += it.second;
    }
  }
  vector< int64 > add(N);
  for(auto v : rot) add[v.first - 1] += v.second;
  for(int i = N - 2; i >= 0; i--) add[i] += add[i + 1];
  for(int i = 0; i < N; i++) cout << add[i] << endl;
}