Sherlock Holmes has determined that the Grand Conspiracy Signal ($$$\mathcal{G}$$$) for any group of $$$k$$$ suspects chosen from the range $$$[l, r]$$$ is not merely the xor of their codes, but a complex interaction of their indices' internal bitwise structures.
Formal Definition Given an array $$$a$$$ of size $$$n$$$, and $$$q$$$ operations (updates or queries), define the Grand Conspiracy Signal for a range $$$[l, r]$$$ and subset size $$$k$$$ as:$$$$$$\mathcal{G}(l, r, k) = = \bigoplus_{l \le i_1 \lt i_2 \lt \dots \lt i_k \le r} \left( a_{\left( \bigoplus_{j_1 \subseteq i_1} j_1 \right)} \oplus a_{\left( \bigoplus_{j_2 \subseteq i_2} j_2 \right)} \oplus \dots \oplus a_{\left( \bigoplus_{j_k \subseteq i_k} j_k \right)} \right)$$$$$$
Where:
$$$\bigoplus$$$ denotes the bitwise XOR operation.
$$$j \subseteq i_m$$$ denotes that $$$j$$$ is a bitwise submask of $$$i_m$$$.
The outermost XOR sum is taken over all possible combinations of $$$k$$$ distinct indices within the interval $$$[l, r]$$$.
Operations :
1. Update($$$pos, val$$$): Change the suspect's cipher code at index $$$pos$$$ such that $$$a_{pos} = val$$$.
2. Query($$$l, r, k$$$): Calculate the current value of $$$\mathcal{G}(l, r, k)$$$.
The first line contains two integers $$$n$$$ and $$$q$$$ ($$$1 \le n, q \le 2 \cdot 10^5$$$) — the number of suspects and the number of operations.
The second line contains $$$n$$$ integers $$$a_0, a_1, \dots, a_{n-1}$$$ ($$$0 \le a_i \lt 2^{30}$$$) — the Cipher Code of each suspect.
Each of the next $$$q$$$ lines describes an operation:
• $$$1\ \text{pos}\ \text{val}$$$ — Watson updates the evidence. Set the Cipher Code of suspect $$$\text{pos}$$$ to $$$\text{val}$$$ ($$$0 \le pos \le n-1, 0 \le val \lt 2^{30}$$$).
• $$$2\ l\ r\ k$$$ — Holmes asks for the Grand Conspiracy Signal $$$\mathcal{G}(l, r, k) .$$$ ($$$0 \le l \le r \le n-1$$$ , $$$ 2 \le k \le r-l+1 $$$ ).
For each operation of type 2, output a single integer — the Grand Conspiracy Signal .
5 41 2 3 4 52 1 4 22 2 4 21 2 32 1 4 2
5 0 5
