Upper bound on the right tail of $bin(n,p)$ evaluated at $k

Question

Consider a binomial RV $N \sim bin(n,p)$.

I am interested in finding an $\textbf{upper bound}$ to the complementary CDF given by:

$\hspace{2.5in}P(N\geq k)$ where $k=np-m$ and $m \in \mathbb{Z}^{+}$.

Note that this means that the point of evaluation ($k$) is below the expected value $(np)$.

I searched in a number of resources but all of those talk about upper bounds when $k\geq np$. For example,

1. https://en.wikipedia.org/wiki/Binomial_distribution#Tail_bounds
2. Sharper Lower Bounds for Binomial/Chernoff Tails

Can someone help me find a useful upper bound when $k<np$.?