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;
#define ll long long
#define N 100010
int q, n, num;
ll len[N], val[N], ans[N], x;
void search(ll x, ll v) {
    if (x == 0) return;
    int add = upper_bound(len + 1, len + num + 1, x) - len - 1;
    if (add) {
        val[add] += (x / len[add]) * v;
        search(x % len[add], v);
    } else
        ans[1] += v, ans[x + 1] -= v;
}
int main() {
    scanf("%d%d", &n, &q);
    len[++num] = n;
    while (q--) {
        scanf("%lld", &x);
        while (num && len[num] >= x) num--;
        len[++num] = x;
    }
    val[num] = 1;
    for (ll i = num - 1; i; i--) {
        val[i] += len[i + 1] / len[i] * val[i + 1];
        search(len[i + 1] % len[i], val[i + 1]);
    }
    ans[1] += val[1], ans[len[1] + 1] -= val[1];
    for (ll i = 1; i <= n; i++) printf("%lld\n", ans[i] += ans[i - 1]);
    return 0;
}