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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.ABC_150
{
    class F
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            int[] aArray = ReadInts();
            int[] bArray = ReadInts();
            int[] aDeltas = new int[2 * n];
            int[] bDeltas = new int[n];
            for (int i = 0; i < n; i++)
            {
                aDeltas[i] = aArray[i % n] ^ aArray[(i + 1) % n];
                aDeltas[i + n] = aDeltas[i];
                bDeltas[i] = bArray[i % n] ^ bArray[(i + 1) % n];
            }

            RollingHash aHash = new RollingHash(aDeltas);
            RollingHash bHash = new RollingHash(bDeltas);
            for(int i = 0; i < n; i++)
            {
                if(bHash.ValidateRange(0, n, aHash.GetRangeHash(i, n)))
                {
                    WriteLine(i + " " + (aArray[i] ^ bArray[0]));
                }
            }
        }

        class RollingHash
        {
            long mod = 1000000007;
            long[] bases = new long[3] { 1009, 2003, 3001 };
            long[,] pows;
            long[,] hashes;

            public RollingHash(int[] s)
            {
                pows = new long[s.Length, bases.Length];
                hashes = new long[s.Length, bases.Length];

                for (int i = 0; i < s.Length; i++)
                {
                    for (int j = 0; j < bases.Length; j++)
                    {
                        if (i == 0) pows[i, j] = 1;
                        else pows[i, j] = (pows[i - 1, j] * bases[j]) % mod;
                    }
                }

                for (int i = 0; i < s.Length; i++)
                {
                    for (int j = 0; j < bases.Length; j++)
                    {
                        if (i > 0) hashes[i, j] = (hashes[i - 1, j] * bases[j]) % mod;
                        hashes[i, j] += s[i];
                        hashes[i, j] %= mod;
                    }
                }
            }

            public long[] GetRangeHash(int l, int length)
            {
                long[] hash = new long[bases.Length];
                for (int i = 0; i < bases.Length; i++)
                {
                    hash[i] = hashes[l + length - 1, i];
                    if (l > 0)
                    {
                        hash[i] += mod - (hashes[l - 1, i] * pows[length, i]) % mod;
                        hash[i] %= mod;
                    }
                }
                return hash;
            }

            public bool ValidateRange(int l, int length, long[] hash)
            {
                int r = l + length - 1;
                long[] rangeHash = GetRangeHash(l, length);
                for (int i = 0; i < bases.Length; i++)
                {
                    if (rangeHash[i] != hash[i]) return false;
                }
                return true;
            }

            public long[] GetStringHash(string s)
            {
                long[] vals = new long[bases.Length];
                for (int i = 0; i < s.Length; i++)
                {
                    for (int j = 0; j < bases.Length; j++)
                    {
                        vals[j] = (vals[j] * bases[j] + s[i]) % mod;
                    }
                }

                return vals;
            }
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}