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 Go (1.6) (judge verdict: Accepted)

package main
import (
  "bufio"
  "os"
  "strconv"
  "strings"
  "fmt"
)

var reader = bufio.NewReaderSize(os.Stdin, 1000000)
var writer = bufio.NewWriter(os.Stdout)
func NextLine() string {
  buffer := make([]byte, 0)
  for true {
    line, isPrefix, err := reader.ReadLine()
    if err != nil { panic(err) }
    buffer = append(buffer, line...)
    if !isPrefix { break }
  }
  return string(buffer)
}
func NextInt() int {
  n, _ := strconv.Atoi(NextLine())
  return n
}
func NextIntVec() []int {
  L := strings.Split(NextLine(), " ")
  N := make([]int, len(L))
  for i := range N {
    N[i], _ = strconv.Atoi(L[i])
  }
  return N
}
func Write(s interface{}) {
  fmt.Fprintln(writer, s)
}
func WriteIntVec(A []int) {
  S := make([]string, len(A))
  for i, a := range A {
    S[i] = strconv.Itoa(a)
  }
  Write(strings.Join(S, " "))
}
func Output() {
  _ = writer.Flush()
}

func KMP(A, B []interface{}) []int {
  N := len(B)
  PMT := make([]int, N + 1)
  PMT[0] = -1
  for i, j := 2, 0; i <= N; {
    if B[i - 1] == B[j] {
      PMT[i] = j + 1
      i++
      j++
    } else if 0 < j {
      j = PMT[j]
    } else {
      PMT[i] = 0
      i++
    }
  }
  M := make([]int, 0)
  for i, j := 0, 0; i + j < len(A); {
    if A[i + j] == B[j] {
      j++
      if j == N {
        M = append(M, i)
        i += N - PMT[N]
        j = PMT[j]
      }
    } else {
      i += j - PMT[j]
      if 0 < j { j = PMT[j] }
    }
  }
  return M
}

func main() {
  N := NextInt()
  A := NextIntVec()
  B := NextIntVec()
  XA := make([]interface{}, N)
  XB := make([]interface{}, N)
  for i, a := range A {
    XA[i] = a ^ A[(i + 1) % N]
    XB[i] = B[i] ^ B[(i + 1) % N]
  }
  XA = append(XA, XA...)
  K := KMP(XA, XB)
  for _, k := range K {
    if N <= k { break }
    x := A[k] ^ B[0]
    WriteIntVec([]int{k, x})
  }
  Output()
}