- Time limit: 1.00 s
- Memory limit: 512 MB
You are given an array of n integers. Your task is to calculate the number of non-empty subsets whose elements' bitwise and is equal to k for each k = 0, 1,\dots, n.
Input
The first line has an integer n: the size of the array.
The next line has n integers a_1, a_2,\dots, a_n: the contents of the array.
Output
Print n + 1 integers as specified above modulo 10^9 + 7.
Constraints
- 1 \le n \le 2 \cdot 10^5
- 0 \le a_i \le n
Example
Input:
4 3 1 3 4
Output:
7 4 0 3 1