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>

typedef long long LL;
std::map<LL, LL> M;
typedef std::map<LL, LL>::iterator it;

const int MAXN = 100010;
LL st[MAXN], ansl[MAXN]; int top;
int main() {
	int n, Q; LL t;
	std::cin >> n >> Q;
	st[++top] = n;
	while (Q --> 0) {
		std::cin >> t;
		while (top && t <= st[top]) --top;
		st[++top] = t;
	}
	M[st[top]] = 1;
	auto back = [] () { it t = M.end(); return --t; };
	for (int i = top - 1; i; --i) {
		M[st[i]]; LL at, v; it t;
		while ((t = back())->first > st[i]) {
			at = t->first, v = t->second;
			M[st[i]] += at / st[i] * v;
			M[at % st[i]] += v;
			M.erase(t);
		}
	}
	for (auto t : M) ansl[t.first] += t.second;
	for (int i = n; i; --i) ansl[i] += ansl[i + 1];
	for (int i = 1; i <= n; ++i)
		std::cout << ansl[i] << '\n';
	return 0;
}