Problem Description

Given $ N $ distinct integers $ a_1, a_2, ..., a_N $ and an integer $ M $.

For each integer $ i $ from $ 1 $ to $ M $, find the number of integers in $ a_1, a_2, ..., a_N $ that are coprime with $ i $.

Input Format

The input is given from the standard input in the following format:

$ N $ $ M $ $ a_1 $ $ a_2 $ $ : $ $ a_N $

Output Format

Output $ M $ lines. The $ i $-th line ($1 \leq i \leq M$) should contain the number of integers in $ a_1, a_2, ..., a_N $ that are coprime with $ i $.

Sample Input and Output

Sample Input #1

4 3
6
7
8
9

Sample Output #1

4
2
2

Sample Input #2

1 5
100000

Sample Output #2

1
0
1
0
0

Sample Input #3

5 7
14142
17320
22360
24494
26457

Sample Output #3

5
1
3
1
3
0
5

Notes/Hints

Annotation

Two integers $ a $ and $ b $ are coprime if there is no positive integer other than $ 1 $ that divides both $ a $ and $ b $.

For example, $ 6 $ and $ 7 $ are coprime, but $ 6 $ and $ 8 $ are not coprime because they are both divisible by $ 2 $.

Constraints

• $1 \leq N, M \leq 10^5$
• $1 \leq a_i \leq 10^5$
• All $ a_i $ are distinct.
• All input values are integers.

Sample Explanation 1

Among $ 6, 7, 8, 9 $:
- Those coprime with $ 1 $ are $ 6, 7, 8, 9 $ (4 numbers)
- Those coprime with $ 2 $ are $ 7, 9 $ (2 numbers)
- Those coprime with $ 3 $ are $ 7, 8 $ (2 numbers)

见题面 Input 部分

见题面 Output 部分