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 ll = long long;
const int N = 1e5 + 9;

int n, q, t, i;
ll s[N], ans[N], f[N] , j, k;

int main () {
	scanf("%d%d", &n, &q);
	s[t = 1] = n;
	for (i = 1; i <= q; ++i) {
		scanf("%lld", &j);
		while (t && j <= s[t]) --t; s[++t] = j;
	}
	f[t] = 1;
	for (i = t; i > 0; --i) {
		k = s[i], j = i;
		while ((j = lower_bound(s + 1, s + j + 1, k) - s - 1) > 0) {
			f[j] += k / s[j] * f[i];
			k %= s[j];
		}
//		ans[n] += k / n * f[i];
//		ans[k % n] += f[i];
		ans[k] += f[i];
	}
	for (i = n - 1; i; --i) ans[i] += ans[i + 1];
	for (i = 1; i <= n; ++i) printf("%lld\n", ans[i]);
	return 0;
}