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;

const int N = 1e5 + 10;

long long st[N], delta[N], coef[N];
int n, top, Q;

void solve(long long val, long long coef) {
  int ind = upper_bound(st + 1, st + top + 1, val) - st - 1;
  if(!ind) {
    delta[1] += coef;
    delta[val + 1] -= coef;
  } else {
    ::coef[ind] += val / st[ind] * coef;
    solve(val % st[ind], coef);
  }
}

int main(void) {
  scanf("%d%d", &n, &Q);
  st[++top] = n;
  for(int i = 1; i <= Q; i++) {
    long long x;
    scanf("%lld", &x);
    while(top && st[top] >= x) {
      top--;
    }
    st[++top] = x;
  }
  coef[top] = 1;
  for(int i = top; i > 1; i--) {
    coef[i - 1] += st[i] / st[i - 1] * coef[i];
    solve(st[i] % st[i - 1], coef[i]);
  }
  delta[1] += coef[1];
  delta[st[1] + 1] -= coef[1];
  for(int i = 1; i <= n; i++) {
    printf("%lld\n", delta[i] += delta[i - 1]);
  }
  return 0;
}