Let \oplus denote the xor binary operation. Define x \star y=(x+y)-(x \oplus y). Compute
\sum_{k=1}^{63}(k \star 45)
(Remark: The xor operator works as follows: when considered in binary, the k th binary digit of a \oplus b is 1 exactly when the k th binary digits of a and b are different. For example, 5 \oplus 12=0101_{2} \oplus 1100_{2}=1001_{2}=9.)