Subset Sum I

Problem Description

You are given an integer $n$. Define $f_0 = 1$, and for all $i \in [1, 2^n)$, $f_i = \sum_{j \& i = j, j < i} f_j \times i \mod 1000000007$. Output $f_0, f_1, ..., f_{2^n-1}$ in order.

Input Format

One line containing an integer $n$.

Output Format

Output one line containing $2^n$ integers: the answer.

Sample Input

2

Sample Output

1 1 2 12

Constraints

For all data, $1 \le n \le 16$.