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Possible Duplicate:
XOR properties in set of numbers

Say I have n positive numbers $A_1$,$A_2$...$A_n$ and $A_k$ is minimum among them. And d is a number such that ($A_1$-d) $\oplus$ ($A_2$-d) $\oplus$ .......(An-1-d) $\oplus$ ($A_n$-d) = 0 where 0<=d <= $A_k$ .

I want to know how many d are there . I know I can iterate all possible value of d and take XOR of n number every time and find out but complexity in this case is O($A_k*n$) which is O($n^2$) in worst case.

Is their any property of XOR which can help us to find number of d in less complexity than this ?

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