Problem:
Score : 600 points

Problem Statement

Given are two sequences a=\{a_0,\ldots,a_{N-1}\} and b=\{b_0,\ldots,b_{N-1}\} of N non-negative integers each.

Snuke will choose an integer k such that 0 \leq k < N and an integer x not less than 0, to make a new sequence of length N, a'=\{a_0',\ldots,a_{N-1}'\}, as follows:

a_i'= a_{i+k \mod N}\ XOR \ x

Find all pairs (k,x) such that a' will be equal to b.

What is \mbox{ XOR }?

The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:

When A \mbox{ XOR } B is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.

For example, 3 \mbox{ XOR } 5 = 6. (In base two: 011 \mbox{ XOR } 101 = 110.)

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq a_i,b_i < 2^{30}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_0 a_1 ... a_{N-1}
b_0 b_1 ... b_{N-1}

Output

Print all pairs (k, x) such that a' and b will be equal, using one line for each pair, in ascending order of k (ascending order of x for pairs with the same k).

If there are no such pairs, the output should be empty.

Sample Input 1

3
0 2 1
1 2 3

Sample Output 1

1 3

If (k,x)=(1,3),

a_0'=(a_1\ XOR \ 3)=1

a_1'=(a_2\ XOR \ 3)=2

a_2'=(a_0\ XOR \ 3)=3

and we have a' = b.

Sample Input 2

5
0 0 0 0 0
2 2 2 2 2

Sample Output 2

0 2
1 2
2 2
3 2
4 2

Sample Input 3

6
0 1 3 7 6 4
1 5 4 6 2 3

Sample Output 3

2 2
5 5

Sample Input 4

2
1 2
0 0

Sample Output 4

No pairs may satisfy the condition.

Solution in Rust (1.42.0) (judge verdict: Accepted)

struct MP {
    next: Vec<i32>,
}

impl MP {
    fn new(s: &Vec<usize>) -> MP {
        let n = s.len();
        let mut next = Vec::with_capacity(n + 1);
        next.push(-1);
        let mut j = -1;
        for i in 0..n {
            while j >= 0 && s[i] != s[j as usize] {
                j = next[j as usize];
            }
            j += 1;
            next.push(j);
        }

        MP { next }
    }
}

fn main() {
    let n: usize = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        buf.trim_end().parse().unwrap()
    };
    let a: Vec<usize> = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let iter = buf.split_whitespace();
        iter.map(|x| x.parse().unwrap()).collect()
    };
    let b: Vec<usize> = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let iter = buf.split_whitespace();
        iter.map(|x| x.parse().unwrap()).collect()
    };

    let c: Vec<usize> = {
        let mut c = Vec::with_capacity(n * 2);
        for i in 0..(n * 2) {
            c.push(a[i % n] ^ a[(i + 1) % n]);
        }
        c
    };
    let d: Vec<usize> = {
        let mut d = Vec::with_capacity(n);
        for i in 0..n {
            d.push(b[i % n] ^ b[(i + 1) % n]);
        }
        d
    };

    let mp = MP::new(&d);
    
    let mut i = 0;
    for j in 0..(c.len() - 1) {
        while i >= 0 && c[j] != d[i as usize] {
            i = mp.next[i as usize];
        }
        i += 1;
        if i == n as i32 {
            let k = j - (n - 1);
            println!("{} {}", k, a[k] ^ b[0]);
            i = mp.next[i as usize];
        }
    }
}