Complete solution space
Work over \(\mathbb F_p\), where \(p=1\,000\,000\,007\). Given (A\) and
(b), describe every solution of
\[
Ax=b.
\]
Input
The first line contains (n,m). The next (n) lines contain the (n\times m)
matrix (A). The final line contains (b\in\mathbb F_p^n).
Output
Print `NO` if the system is inconsistent. Otherwise print `YES`, one particular
solution (x_0) of length (m), then an integer (k), followed by (k)
vectors of length (m). The vectors must form a basis of \(\ker(A)\). Thus all
solutions are exactly
\[
x=x_0+\lambda_1v_1+\cdots+\lambda_kv_k.
## Constraints
- \(1\le n,m\le 200\)
- Every entry of \(A\) and \(b\) is an integer in \([0,p)\)
\]