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;
const int N = 100054;

int n, q, top = 1;
ll s[N], coef[N], ans[N];

int main() {
	int i, j; ll x; lldiv_t z;
	scanf("%d%d", &n, &q), s[1] = n;
	for (; q; s[++top] = x, --q)
		for (scanf("%lld", &x); top && s[top] >= x; --top);
	coef[top] = 1;
	for (i = top; i; ans[x] += coef[i], --i)
		for (x = s[j = i]; (j = std::upper_bound(s + 1, s + j, x) - s - 1) > 0; x = z.rem)
			z = lldiv(x, s[j]), coef[j] += z.quot * coef[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;
}