  For integers $n, m$ with $n \geq 1$ and $0 \leq m \leq n$, an $(n,m)$-Dyck
path is a lattice path in the integer lattice $\mathbb{Z} \times \mathbb{Z}$
using up steps $(0,1)$ and down steps $(1,0)$ that goes from the origin $(0,0)$
to the point $(n,n)$ and contains exactly $m$ up steps below the line $y=x$.
The classical Chung-Feller theorem says that the total number of $(n,m)$-Dyck
path is independent of $m$ and is equal to the $n$-th Catalan number
$C_n=\frac{1}{n+1}{2n \choose n}$. For any integer $k$ with $1 \leq k \leq n$,
let $p_{n,m,k}$ be the total number of $(n,m)$-Dyck paths with $k$ peaks. Ma
and Yeh proved that $p_{n,m,k}$=$p_{n,n-m,n-k}$ for $0 \leq m \leq n$, and
$p_{n,m,k}+p_{n,m,n-k}=p_{n,m+1,k}+p_{n,m+1,n-k}$ for $1 \leq m \leq n-2$. In
this paper we give bijective proofs of these two results. Using our bijections,
we also get refined enumeration results on the numbers $p_{n,m,k}$ and
$p_{n,m,k}+p_{n,m,n-k}$ according to the starting and ending steps.
