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)

ARG_N = gets.to_i
ARG_a = gets.split.map(&:to_i)
ARG_b = gets.split.map(&:to_i)
xa, xb = Array.new(ARG_N), Array.new(ARG_N)
i = 0
OVER = 2**31
while i < ARG_N do
  xa[i] = ARG_a[i] ^ ARG_a[i-1]
  xb[i] = ARG_b[i] ^ ARG_b[i-1]
  i+=1
end
xa += xa
results = []

def kmp_table arr 
  result = Array.new(arr.length)
  result[0] = 0
  j = 0
  1.upto(arr.length-1) do |i|
    result[i] = j
    if arr[i] == arr[j]
      j+=1
    else
      j= 0
    end
  end
  result[arr.length] = j
  result
end

table = kmp_table(xb)
# p xb
# p table

i = 0
j = 0
while i < (ARG_N * 2) -1 do
  # p [i,j]
  if xa[i] == xb[j]
    i+=1
    j+=1
  elsif j == 0
    i+=1
  else
    j = table[j]
  end
  if j == ARG_N
    r = (i-j) % ARG_N
    results.push([r, ARG_a[r]^ARG_b[0]])
    j = table[j]
  end
end
results.each do |re|
  puts "#{re[0]} #{re[1]}"
end