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 Julia (0.5.0) (judge verdict: Time Limit Exceeded)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
	p = 10^9+7
	n = readline() |> parseInt
	a = readline() |> split |> parseMap
	b = readline() |> split |> parseMap
	c = zeros(Int,n)
	d = zeros(Int,n)
	for i in 1:n-1
		c[i]=a[i]$a[i+1]
		d[i]=b[i]$b[i+1]
	end
	c[n]=a[1]$a[n]
	d[n]=b[1]$b[n]
	z = 103
	za = zeros(Int,n+1)
	za[1]=1
	for i in 2:n+1
		za[i]=za[i-1]*z%p
	end
	rhc=c[1]*za[n]%p
	rhd=d[1]*za[n]%p
	for i in 2:n
		rhc=(rhc+(c[i]*za[n-i+1])%p)%p
		rhd=(rhd+(d[i]*za[n-i+1])%p)%p
	end
	hash = rhc
	if hash==rhd
		f = 0
		for i in 1:n
			if c[i]!=d[i]
				f = 1
				break
			end
		end
		if f == 0
			println("0"," ",a[1]$b[1])
		end
	end
	for i in 1:n-1
		hash = (mod(hash-za[n]*c[i],p)*z%p+c[i])%p
		if hash==rhd
			f = 0
			for j in 0:n-1
				if c[(i+j)%n+1]!=d[j+1]
					f = 1
					break
				end
			end
			if f == 0
				println(i," ",a[i%n+1]$b[1])
			end
		end
	end
end

main()