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>
#define N 110000
#define LL long long
using namespace std;
LL sta[N],a[N],t[N],s[N],ans;
int tp,n,m;
int td(LL k,int r)
{
    int l=1,res=0;
    while(l<=r)
    {
        int mid=(l+r)/2;
        if(a[mid]<=k) res=mid,l=mid+1;
        else r=mid-1;
    }
    return res;
}
int main()
{
    scanf("%d%d",&n,&m);
    sta[tp=1]=n;
    for(int i=1;i<=m;i++)
    {
        LL x;scanf("%lld",&x);
        while(x<=sta[tp]) tp--;
        sta[++tp]=x;
    }
    m=tp;
    for(int i=1;i<=m;i++) a[i]=sta[i];
    t[m]=1;
    for(int i=m;i>=1;i--)
    {
        LL k=a[i];int p=td(k,i-1);
        while(p)
        {
            t[p]+=(k/a[p])*t[i];
            k%=a[p];
            p=td(k,p-1);
        }
        s[1]+=t[i];s[k+1]-=t[i];
    }
    for(int i=1;i<=n;i++) {ans+=s[i];printf("%lld\n",ans);}
    return 0;
}