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)

#region いつもの
#pragma warning disable
using System;
using System.Collections.Generic;
using System.Linq;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using static AtCoderProject.Global;

namespace AtCoderProject
{
    static class Global
    {
        private class ComparerReverseImpl<T> : Comparer<T> where T : IComparable<T> { public override int Compare(T y, T x) => x.CompareTo(y); public override bool Equals(object obj) => obj != null && GetType() == obj.GetType(); public override int GetHashCode() => GetType().GetHashCode(); }
        public static IComparer<T> ComparerReverse<T>() where T : IComparable<T> => new ComparerReverseImpl<T>();
        public static BigInteger ParseBigInteger(string s)
        {
            // MonoのBigInteger.Parseが遅いので自前実装
            var res = BigInteger.Zero;
            var splited = new string[(s.Length + 7) / 8];
            for (int i = 0; i < splited.Length - 1; i++)
            {
                splited[i] = s.Substring(8 * i, 8);
            }
            splited[splited.Length - 1] = s.Substring(8 * (splited.Length - 1));
            foreach (var sp in splited)
            {
                res *= (int)Math.Pow(10, sp.Length);
                res += int.Parse(sp);
            }
            return res;
        }
        public static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
        public static string AllJoin<T>(IEnumerable<T> source) => string.Join(" ", source);
    }
    static class Ext
    {
        public static T[][] Chunk<T>(this T[,] source)
        {
            var len0 = source.GetLength(0);
            var len1 = source.GetLength(1);
            var res = new T[len0][];
            for (int i = 0; i < len0; i++)
            {
                res[i] = new T[len1];
                for (int j = 0; j < len1; j++)
                {
                    res[i][j] = source[i, j];
                }
            }
            return res;
        }

        public static Tuple<TSource, TMax> MaxBy<TSource, TMax>
            (this IEnumerable<TSource> source, Func<TSource, TMax> maxBySelector)
            where TMax : IComparable<TMax>
        {
            TMax max;
            TSource maxByItem;

            var e = source.GetEnumerator();
            e.MoveNext();
            maxByItem = e.Current;
            max = maxBySelector(maxByItem);
            while (e.MoveNext())
            {
                var item = e.Current;
                var next = maxBySelector(item);
                if (max.CompareTo(next) < 0)
                {
                    max = next;
                    maxByItem = item;
                }
            }
            return Tuple.Create(maxByItem, max);
        }
        public static Tuple<TSource, TMin> MinBy<TSource, TMin>
            (this IEnumerable<TSource> source, Func<TSource, TMin> minBySelector)
            where TMin : IComparable<TMin>
        {
            TMin min;
            TSource minByItem;

            var e = source.GetEnumerator();
            e.MoveNext();
            minByItem = e.Current;
            min = minBySelector(minByItem);
            while (e.MoveNext())
            {
                var item = e.Current;
                var next = minBySelector(item);
                if (min.CompareTo(next) > 0)
                {
                    min = next;
                    minByItem = item;
                }
            }
            return Tuple.Create(minByItem, min);
        }
        public static IComparer<T> Reverse<T>(this IComparer<T> comparer) => Comparer<T>.Create((x, y) => comparer.Compare(y, x));
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
    }
    public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public int Int0 => Int - 1; public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { private string[] splited; public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String => splited; } public SplitLine Split => new SplitLine(this); public class RepeatReader : IEnumerable<ConsoleReader> { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator(); System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator(); public string[] String => this.Select(cr => cr.String).ToArray(); public int[] Int => this.Select(cr => cr.Int).ToArray(); public int[] Int0 => this.Select(cr => cr.Int - 1).ToArray(); public long[] Long => this.Select(cr => cr.Long).ToArray(); public double[] Double => this.Select(cr => cr.Double).ToArray(); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
    public class Program
    {
        [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] private ConsoleReader cr;
        public Program(ConsoleReader consoleReader) { this.cr = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc());

        #endregion
        public object Calc()
        {
            var N = cr.Int;
            var a = cr.Split.Int;
            var b = cr.Split.Int;

            var aDiff = new int[2 * N - 1];
            var bDiff = new int[N];

            for (var j = 0; j < N - 1; j++)
            {
                aDiff[j] = aDiff[j + N] = a[j] ^ a[j + 1];
                bDiff[j] = b[j] ^ b[j + 1];
            }
            aDiff[N - 1] = a[0] ^ a[N - 1];
            bDiff[N - 1] = b[0] ^ b[N - 1];

            var table = CreateTable(bDiff);
            var ks = new List<int>();

            int i = 0;
            int p = 0;
            // 文字列探索
            while (i < aDiff.Length && p < bDiff.Length)
            {
                if (aDiff[i] == bDiff[p])
                {
                    i++; p++;
                }
                else if (p != 0)
                {
                    p = table[p];
                }
                else i++;

                if (p == bDiff.Length)
                {
                    ks.Add(i - p);
                    p = table[p];
                }
            }

            foreach (var k in ks)
            {
                Console.WriteLine($"{k} {b[0] ^ a[k]}");
            }

            return "";
        }
        int[] CreateTable(int[] search)
        {
            var table = new int[search.Length + 1];
            table[0] = 0;

            var j = 0;
            for (int i = 1; i < search.Length; i++)
            {
                if (search[i] == search[j])
                {
                    table[i] = j++;
                }
                else
                {
                    table[i] = j;
                    j = 0;
                }
            }
            table[search.Length] = j;
            return table;
        }
    }
}