Problem from Russian book

[rsoldo]

Let $a_{1},a_{2},\ldots,a_{n}$ real numbers. Number $a_{k}$ we call $m$-leader if for some $p$ hold:
$a_{k}+a_{k+1}+\ldots+a_{k+p-1}\geq0, 1\leq p\leq m.$
Prove that the sum all $m$-leaders is nonnegative.

P.S. This problem is from book: А.П.Савин, Ю.М. Брук ... Физико - математические олимпиады, 1977.

[waxtep]

1. Let $M$ be a set of $m$-leaders; take $a_k\in M,a_k<0$ with minimum $k$; so

$$\exists p: 1<p\le m, \sum\limits_{i=k}^{i=k+p-1}a_i[a_i\in M]\ge\sum_{i=k}^{i=k+p-1}a_i\ge0$$

2. Take next minimum $j>k+p-1,a_j<0,a_j\in M$, repeat the argument from (1) and so on.