Direct Sums of Modules.

Question

Let $M$ be a finite-dimensional $kG$-module. Let $M_{1},...,M_{n}$ be simple submodules of $M$ such that

$$M= \sum_{i=1}^{n} M_{i}.$$

Show that we have some subset $I \in \{1,2,...,n\}$ such that

$$M = \bigoplus_{i \in I} M_{i}.$$