question on variation of subset sum problem

Hi,

The problem I have is a variation of subset sum. Given $n$ numbers
a_1, a_2 , ..., a_n and b. Does there exists sets S_1 and S_2
disjoint, subsets of {1,2,...,n} such that

Sum_{i in S_1} a_i + 1/2 Sum_{i in S_2} a_i = b ?

I think this is a NP-complete problem but I cant seem to show it. Any
comments would be greatly appreciated. Thanks,

-aman

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