Given the polynomial equation:

$$a_0+a_1x+a_2x^2+...+a_nx^n=0$$

Find the integer solutions to this equation within the range $[1,m]$ (where $n$ and $m$ are positive integers).

Input

The first line contains two integers $n$ and $m$, separated by a space.

The next $n+1$ lines each contain an integer, representing $a_0, a_1, a_2, ..., a_n$ in order.

Output

The first line outputs the number of integer solutions to the equation within the range $[1,m]$.

Each subsequent line contains one integer, outputting the integer solutions found within $[1,m]$ in ascending order.

Examples

Input 1

2 10
1
-2
1

Output 1

1
1

Input 2

2 10
2
-3
1

Output 2

2
1
2

Input 3

2 10
1
3
2

Output 3

0

Constraints

For 30% of the data, $0 < n \le 2$, $|a_i| \le 100$, $a_n \ne 0$, $m \le 100$;

For 50% of the data, $0 < n \le 100$, $|a_i| \le 10^{100}$, $a_n \ne 0$, $m \le 100$;

For 70% of the data, $0 < n \le 100$, $|a_i| \le 10^{10000}$, $a_n \ne 0$, $m \le 10000$;

For 100% of the data, $0 < n \le 100$, $|a_i| \le 10^{10000}$, $a_n \ne 0$, $m \le 1000000$.