I came across this statement and couldn't figure out why this is true, please help:
Let $M$ be an n-dimensional compact, connected, orientable smooth manifold without boundary. Prove that there exists a smooth map $f:M\rightarrow \mathbb{S}^n$ such that $\text{deg}(f) = k$ for arbitrary $k\in \mathbb{Z}$.
Here the degree is defined by $\int_M f^*\omega = \text{deg}(f)\cdot \int_{\mathbb{S}^n} \omega$.