Given $A=\{1,2,3..,n\}$, $B=\{1,2,3,..,m\},$$\space \space $while $5<m,n$ $\space$ and $\space \Omega = \{ \space f \mid f: A \rightarrow B\space \}$

How many functions are monotonically increasing in $\Omega$ while $m>n$?

My answer is $m-n+1$. 

Basic example is $A=\{1,2,3,4,5\}$ and $B=\{1,2,3,4,5,6\}$.
hence:
$$f\_1(1) = 1, \space \space f\_1(2) = 2, \space \space f\_1(3) = 3, \space \space f\_1(4) = 4, \space \space f\_1(5) = 5$$
$$f\_2(1) = 2, \space \space f\_2(2) = 3, \space \space f\_2(3) = 4, \space \space f\_2(4) = 5, \space \space f\_2(5) = 6$$

So we get 2 functions, and while the diffrence between $m$ and $n$ getting bigger, the result's getting bigger.
Am I missing somthing?