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>
const int maxn = 100100;
typedef long long ll;
std::map<ll, ll> map;
int q;
ll a[maxn], s;
ll ans[maxn];
int main() {
	std::ios::sync_with_stdio(false), std::cin.tie(0);
	std::cin >> *a >> q;
	for(int i = 1;i <= q;++i) std::cin >> a[i];
	map[a[q]] = 1;
	for(int i = q - 1;i >= 0;--i) {
		auto it = map.upper_bound(a[i]);
		for(auto j = it;j != map.end();++j) { 
			map[a[i]] += j -> first / a[i] * j -> second;
			map[j -> first % a[i]] += j -> second;
		}
		map.erase(it, map.end());
	}
	for(int i = *a;i >= 1;--i) ans[i] = ans[i + 1] + map[i];
	for(int i = 1;i <= *a;++i) std::cout << ans[i] << '\n';
}