XORanges

Janez loves oranges! So he made a scanner for oranges. With cameras and a Raspberry Pi 3b+ computer, he started creating 3D images of oranges. His image processor is not a very good one, so the only output he gets is a $32$-bit integer, which holds information about the holes on the peel. A $32$-bit integer $D$ is represented as a sequence of $32$ digits (bits) each of which is one or zero. If we start from $0$ we can obtain the number by adding 2^i for every $i$-th bit that is equal to one. More formally the number $D$ is represented by the sequence d_{31},d_{30}, ..., d_0, when D = d_{31} \cdot 2^{31} + d_{30} \cdot 2^{30} + ... + d_1 \cdot 2^1 + d_0 \cdot 2^0. For example, $13$ is represented as 0, ..., 0, 1, 1, 0, 1.

Janez scanned $n$ oranges; however, sometimes he decides to rescan one of the oranges ($i$-th orange) during the execution of your program. This means that from this scan on, he uses the updated value for the $i$-th orange.

Janez wants to analyse those oranges. He finds exclusive or (XOR) operation very interesting, so he decides to make some calculations. He selects a range of oranges from $l$ to $u$ (where l \le u) and wants to find out the value of XOR of all elements in that range, all pairs of consecutive elements in that range, all sequences of $3$ consecutive elements and so on up to the sequence of u - l + 1 consecutive elements (all elements in the range).

If l = 2 and u = 4 and there is an array of scanned values $A$, program should return the value of a_2 \oplus a_3 \oplus a_4 \oplus (a_2 \oplus a_3) \oplus (a_3 \oplus a_4) \oplus (a_2 \oplus a_3 \oplus a_4), where $\oplus$ represents the XOR and a_i represents the $i$-th element in array $A$.

Let XOR operation be defined as:

• If the $i$-th bit of the first value is the same as the $i$-th bit of the second value, the $i$-th bit of the result is $0$;

• If the $i$-th bit of the first value is different from the $i$-th bit of the second value, the $i$-th bit of the result is $1$.

For example, 13 \oplus 23 = 26.