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;
typedef long long ll;
int main()
{
    int n, q;
    scanf("%d%d", &n, &q);
    vector < ll > Q = {n};
    for (; q; q --)
    {
        ll a;
        scanf("%lld", &a);
        while (Q.size() && Q.back() >= a)
            Q.pop_back();
        Q.push_back(a);
    }
    map < ll , ll > M;
    M[Q.back()] ++;
    for (int i = (int)Q.size() - 2; ~ i; i--)
        while (M.rbegin()->first > Q[i])
        {
            ll a = M.rbegin()->first, b = M.rbegin()->second;
            M[Q[i]] += a / Q[i] * b;
            M[a % Q[i]] += b;
            M.erase(a);
        }
    for (int i = n; i; i--)
        M[i] += M[i + 1];
    for (int i = 1; i <= n; i++)
        printf("%lld\n", M[i]);
    return 0;
}