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 Ruby (2.3.3) (judge verdict: Accepted)

B = (1e6 + 7).to_i
H = (1e9 + 7).to_i

def gen_hash(m, n, s)

  hash = 0
  n.times do |i|
    hash = hash * B + s[i]
    hash %= H
  end

  hash
end

def main
  n = gets.chomp.to_i
  a = gets.chomp.split.map(&:to_i)
  a[n] = a[0]
  b = gets.chomp.split.map(&:to_i)
  b[n] = b[0]
  
  axa = []
  bxa = []
  #a+k xor a+1+k = b xor b+1 となるkを見つける
  bXor = b[0] ^ b[1]
  k = []
  n.times do |i|
    #a[i]xor a[i+1]の配列を作る 
    ax = a[i] ^ a[i+1]
    bx = b[i] ^ b[i+1]
    
    axa[i] = ax
    axa[i+n] = ax
    bxa[i] = bx
 
    if ax == bXor
      k.push(i)
    end
  end

  #全ての要素に対してa+k xor b = Xとなるかを確認する
  #ローリングハッシュで検索する
  b_hash = gen_hash(0, n, bxa)
  a_hash = gen_hash(0, n, axa)

  hash_back = 1
  n.times do
    hash_back *= B
    hash_back %= H
  end

  (n).times do |i|
    if a_hash == b_hash
      x = a[i] ^ b[0]
      puts "#{i} #{x}"
    end

    a_hash = a_hash * B + axa[n+i] - axa[i] * hash_back
    a_hash %= H
  end

end
 
main