Solve a linear system
Work in the finite field
\[
\mathbb{F}_p, \qquad p = 1\,000\,000\,007.
\]
You are given an \(n \times m\) matrix \(A\) and a vector \(b\) of length
\(n\). Determine whether the system
\[
A x = b
\]
has a solution \(x \in \mathbb{F}_p^m\).
If there are several solutions, you may output any one of them.
Input
The first line contains \(n\) and \(m\). The next \(n\) lines contain \(A\),
with \(m\) entries per line. The final line contains the \(n\) entries of
\(b\).
Output
If the system is inconsistent, print:
NO
Otherwise print `YES` followed by one line containing \(m\) values of a vector
\(x\) satisfying \(A x=b\) modulo \(p\).
All entries are reduced modulo \(p\); any integer representative is accepted.