Judicious XORcery | MatCom Online Grader

The 2025 ICPC Caribbean Finals (Qualifier) - Real Contest

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J - Judicious XORcery

Languages: C, C++, Java, Python, Kotlin

Time & Memory limits: (details)

<div style="text-align: justify">
Axel the XORcerer is brewing a potion to become wiser. The cauldron he uses is divided into $n$ contiguous sections, each with a magic value $a_1, a_2, \dots, a_n$. He needs to stir the potion and add ingredients to specific sections, and he also wants to be able to check the magic value of any section so he can adjust his brew on the fly.

He has a mixing rod, which starts in the first section. The rod can only move to a section immediately adjacent to its current position, either to the left or to the right, if such a section exists. When Axel moves it, the magic values change automatically depending of the direction: </div>

* Single step to the **right**: The rod is in section $i$ ($1 \le i \le n-1$) and Axel moves it to section $i+1$, then  
$a_{i+1} := a_{i+1} \oplus a_i$
* Single step to the **left**: The rod is in section $i$ ($2 \le i \le n$) and Axel moves it to section $i-1$, then  
$a_i := a_i \oplus a_{i-1}$

<div style="text-align: justify">
The $\oplus$ operator refers to bitwise exclusive or (xor).

Moving the rod $k$ times in any direction means applying the corresponding single step (to the right or to the left) sequentially $k$ times. For example, let the initial magic values $a = [\mathbf{2},1,5,4]$ (rod in section 1). If Axel has to move the rod 3 times to the right:
</div>

* Move 1: from section 1 to section 2
    * Apply $a_2 := a_2 \oplus a_1 \rightarrow a_2 = 1 \oplus 2 = 3$
    * Magic values become $[2, \mathbf{3}, 5, 4]$ (rod in section 2)
* Move 2: from section 2 to section 3
    *  Apply $a_3 := a_3 \oplus a_2 \rightarrow a_3 = 5 \oplus 3 = 6$
    * Magic values become $[2,3, \mathbf{6},4]$ (rod in section 3)
* Move 3: from section 3 to section 4
    * Apply $a_4 := a_4 \oplus a_3 \rightarrow a_4 = 4 \oplus 6 = 2$
    * Magic values become $[2,3,6,\mathbf{2}]$ (rod in section 4)

The Axel assistant (in this case, you) will do all the hard work. Axel may give you three types of instructions:
- **1 k** - Move the mixing rod $k$ times to the right if $k > 0$, or $|k|$ times to the left if $k < 0$. Axel ensures $k \neq 0$ and the rod will stay inside the cauldron (it won't go outside the limits 1 to n).
- **2 p x** - Change the magic value of section $p$ to $x$, i.e., $a_p := x$.
- **3 p** - Axel will ask you to report the current magic value of section $p$.

Input

Output

Sample test(s)

Input

4 4 2 1 5 4 1 3 3 4 1 -2 3 3

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Output

2 5

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Input

7 10 3 1 2 10 8 8 7 1 5 2 6 5 3 7 1 -2 3 6 2 3 4 3 7 3 4 1 -1 3 4

--- Showing first 30 lines (click "Copy" to get full content) ---

Output

7 7 7 10 14

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Matcom Online Grader

The 2025 ICPC Caribbean Finals (Qualifier) - Real Contest

Ended

J - Judicious XORcery

Languages: C, C++, Java, Python, Kotlin

Time & Memory limits: (details)

Input

Output

Sample test(s)