Partition a multiset into pairs that sum up to given numbers?

Question

Given a multiset of $2m$ positive numbers, $S=\{s_1,s_2,\ldots,s_{2m}\}$ and given $m$ targets $t_1,t_2,\ldots,t_m$. Can we partition $S$ into $m$ pairs $(a_i,b_i)$ such that $a_i+b_i=t_i$, where $a_i\ne b_i$ and $a_i,b_i\in S$?

For example for $S=\{1,4,6,1,2,5\}$ and $t_1=7$, $t_2=t_3=6$. The answer is YES and the pairs are $(1,6)$, $(2,4)$, and $(1,5)$.