Suppose, \( n, m \) are natural number and \[ f(x)=\left|\begin{array}{ccc} 1 & (1+x)^{m} & (1+m...

Suppose, \( n, m \) are natural number and
\[
f(x)=\left|\begin{array}{ccc}
1 & (1+x)^{m} & (1+m x)^{m n} \\
(1+m x)^{n} & 1 & (1+n x)^{m n} \\
(1+n x)^{m} & (1+x)^{n} & 1
\end{array}\right|
\]
Constant term of the polynomial \( f(x) \) is
(a) 1
(b) \( m+n \)
(c) \( m-n \)