KöMaL 2007 B3981

The real numbers $a_i$, $b_i$ ($i=1, 2, \ldots, n$ ) satisfy the following inequalities: $0\le a_n\le a_{n-1}\le \ldots\le a_2\le a_1$, and $a_1\cdot a_2\cdot \ldots\cdot a_k\le b_1\cdot b_2\cdot \ldots\cdot b_k$, if 1$\le k \le n$. Prove that $a_1+\ldots+a_n\le b_1+\ldots+b_n$.