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 <cstdio>
#include <map>
int Q;
long long q[100001], s[100001];
std::map < long long, long long > M;
int main()
{
	scanf("%lld%d", q, &Q);
	for (int i = 1; i <= Q; i++)
		scanf("%lld", q + i);
	M = { { q[Q], 1 } };
	for (int i = Q - 1; ~i; i--)
	{
		auto it = M.upper_bound(q[i]);
		for (auto j = it; j != M.end(); j++)
		{
			M[q[i]] += j -> first / q[i] * j -> second;
			if (j -> first % q[i])
				M[j -> first % q[i]] += j -> second;
		}
		M.erase(it, M.end());
	}
	for (auto &i : M)
		s[i.first] += i.second;
	for (int i = q[0] - 1; i; i--)
		s[i] += s[i + 1];
	for (int i = 1; i <= q[0]; i++)
		printf("%lld\n", s[i]);
	return 0;
}