Sequential operations on Sequence

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

inputFormat

input values are integers.

Input

The input is given from Standard Input in the following format:

N Q q_1 : q_Q

outputFormat

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

样例

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

7
4
4
3
3
2
2
2
0
0

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