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 rep(i,a,b) for(int i = a; i <= b; i++)
#define dep(i,a,b) for(int i = a; i >= b; i--)
using namespace std;
typedef long long LL;
const int N = 1e5 + 10;
int n, m, top = 0;
LL s[N], w[N], st[N];
int main() {
	scanf("%d%d",&n,&m);
	st[top = 1] = n;
	rep(i,1,m) {
		LL x; scanf("%lld",&x);
		while (top && st[top] >= x) top--;
		st[++top] = x;
	}
	w[top] = 1;
	dep(i,top,1) {
		int x = i - 1; LL l = st[i];
		while (x) {
			w[x] += w[i] * (l / st[x]);
			l %= st[x];
			x = upper_bound(st + 1, st + top + 1, l) - st - 1;
		}
		s[l] += w[i];
	}
	dep(i,n,1) s[i] += s[i + 1];
	rep(i,1,n) printf("%lld ",s[i]); printf("\n");
	return 0;
}