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 <iostream>
#include <cstdio>
#include <algorithm>
#define MN 101000

typedef long long ll;
int n, m;
ll q[MN];
int st[MN], top = 0;
ll f[MN], g[MN];

int main()
{
	scanf("%d%d", &n, &m);
	for(int i = 0; i <= m; i++)
	{
		if(i) scanf("%lld", &q[i]);
		else q[0] = n;
		while(top && q[i] <= q[st[top]]) top--;
		st[++top] = i;
	}
	
	for(int i = 1; i <= top; i++) q[i - 1] = q[st[i]];
	top--; f[top] = 1;
	for(int i = top; i >= 1; i--)
	{
		ll x = q[i];
		while(x >= q[0])
		{
			int p = std::upper_bound(q, q + top + 1, x) - q - 1;
			if(p == i) p--;
			f[p] += f[i] * (x / q[p]);
			x %= q[p];
		}
		if(x) g[x] += f[i];
	}
	g[q[0]] += f[0];
	for(int i = n; i >= 1; i--) g[i] += g[i + 1];
	for(int i = 1; i <= n; i++) printf("%lld\n", g[i]);
}