题目描述
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
输入格式
见题面
输出格式
见题面
样例输入
10 10
9
13
18
8
10
10
9
19
22
27
样例输出
7
4
4
3
3
2
2
2
0
0