Problem:
Score : 1400 points

Problem Statement

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.

Sample Input 1

5 3
6
4
11

Sample Output 1

3
3
3
2
0

After the first operation, the sequence becomes: 1,2,3,4,5,1.

After the second operation, the sequence becomes: 1,2,3,4.

After the third operation, the sequence becomes: 1,2,3,4,1,2,3,4,1,2,3.

In this sequence, integers 1,2,3,4,5 appear 3,3,3,2,0 times, respectively.

Sample Input 2

10 10
9
13
18
8
10
10
9
19
22
27

Sample Output 2

7
4
4
3
3
2
2
2
0
0

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

//Be Name Khorgraph, Besmellah Rahmane Rahim, In The Name Of God;
//#include<bits/stweight++.h>
#include<iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <set>
#include <queue>
#include <deque>
#include <map>
#include <stack>
#include<bitset>
#include<list>
#include<cassert>
#include<numeric>
#include <stdio.h>
#include <string.h>
#include<iomanip>
#include<unordered_map>
#include<unordered_set>


using namespace std;

const long long N = 1e5 + 5;
vector<long long> stk;
long long cnt[N];
long long t[N];
long long n, q;

int main() 
{
	for (long long i = 0; i < N; i++)
	{
	//	cnt[i] = 1;
	}
	cin >> n >> q;
	stk.push_back(n);
	for (long long i = 0; i < q; i++)
	{
		long long tmp;
		cin >> tmp;
		while (stk.size() && stk.back() >= tmp)
		{
			stk.pop_back();
		}
		stk.push_back(tmp);
	}
	reverse(stk.begin(), stk.end());
	t[0] = 1;
	for (long long i = 1; i <= stk.size(); i++)
	{
		long long j = i;
		long long tmp = stk[i - 1];
		while (j < stk.size() && tmp >= stk[j])
		{
			t[j] += t[i - 1] * (tmp / stk[j]);
			tmp = tmp % stk[j];
			j++;
		}
		//cout << tmp << endl;
		for (long long j = 0; j < tmp; j++)
		{
			cnt[j] += t[i - 1];
		}
	}
	for (long long i = 0; i < n; i++)
	{
		cout << cnt[i] << endl;
	}


}