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;

#define ll long long

int q;
ll a[100001];
map<ll, ll> mp;

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);

	cin >> a[0] >> q;
	for(int i=1; i<=q; ++i)
		cin >> a[i];
	mp[a[q]]=1;
	for(int i=q-1; ~i; --i) {
		auto it=mp.end();
		while((--it)->first>a[i]) {
			mp[a[i]]+=it->first/a[i]*it->second;
			mp[it->first%a[i]]+=it->second;
			it=mp.erase(it);
		}
	}
	for(int i=a[0]; i; --i)
		mp[i-1]+=mp[i];
	for(int i=1; i<=a[0]; ++i)
		cout << mp[i] << "\n";
}