Suppose that $\displaystyle \sum^\infty_{n=1} u_n = s,$ where series converge conditionally and $\displaystyle s'>s.$ Help me please in proving following assertion: there exists permutation $\displaystyle \sigma:\mathbb{N}\rightarrow \mathbb{N}$ with properties:

1) $\displaystyle u_n\geq 0\implies \sigma(n)=n;$

2) $\displaystyle \sum^\infty_{n=1} u_{\sigma(n)}=s'.$

I can prove that for any sequences of positive numbers, $\displaystyle (b_n), (B_n)$ such that $\displaystyle b_n\rightarrow 0, \ \sum^\infty_{n=1} b_n=\infty, \ 0<B_1<B_2<\ldots<B_n\rightarrow \infty$, there exists a permutation $\displaystyle \sigma:\mathbb{N}\rightarrow \mathbb{N}$, for which

$\displaystyle \forall k\geq 1 \sum^k_{n=1} b_{\sigma(n)}\leq B_k.$

But I can't apply this properly to initial problem