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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i,a,b) for(int i=a;i<b;i++)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define fore(i,a) for(auto &i:a)
#define all(x) (x).begin(),(x).end()

using namespace std; void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); }
typedef long long ll; const int inf = INT_MAX / 2; const ll infl = 1LL << 60;
template<class T>bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; }
template<class T>bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; }
//---------------------------------------------------------------------------------------------------
template<int MOD> struct ModInt {
    static const int Mod = MOD; unsigned x; ModInt() : x(0) { }
    ModInt(signed sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; }
    ModInt(signed long long sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; }
    int get() const { return (int)x; }
    ModInt& operator+=(ModInt that) { if ((x += that.x) >= MOD) x -= MOD; return *this; }
    ModInt& operator-=(ModInt that) { if ((x += MOD - that.x) >= MOD) x -= MOD; return *this; }
    ModInt& operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; }
    ModInt& operator/=(ModInt that) { return *this *= that.inverse(); }
    ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
    ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
    ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
    ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }
    ModInt inverse() const {
        long long a = x, b = MOD, u = 1, v = 0;
        while (b) { long long t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); }
        return ModInt(u);
    }
    bool operator==(ModInt that) const { return x == that.x; }
    bool operator!=(ModInt that) const { return x != that.x; }
    ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; }
};
template<int MOD> ModInt<MOD> operator^(ModInt<MOD> a, unsigned long long k) {
    ModInt<MOD> r = 1; while (k) { if (k & 1) r *= a; a *= a; k >>= 1; } return r;
}
int getrandmax() {
    static uint32_t y = time(NULL);
    y ^= (y << 13); y ^= (y >> 17);
    y ^= (y << 5);
    return abs((int)y);
}
int getrand(int l, int r) { // [l, r]
    return getrandmax() % (r - l + 1) + l;
}
typedef ModInt<1000000007> mint1;
typedef ModInt<1000000009> mint2;
int primes[10] = { 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093 };
bool isShuffle = false;
struct RollingHash {
    mint1 p1; mint2 p2;
    int n;
    vector<mint1> m1; vector<mint2> m2;
    vector<mint1> v1; vector<mint2> v2;

    RollingHash() {
        if (!isShuffle) {
            rep(i, 0, 101) { int a = getrand(0, 9); int b = getrand(0, 9); swap(primes[a], primes[b]); }
            isShuffle = true;
        }
        p1 = primes[0], p2 = primes[1];
    }

    void init(string s, char o = 'a') {
        vector<int> v;
        fore(c, s) v.push_back(c - o);
        init(v);
    }

    void init(vector<int> s) {
        n = s.size();
        m1.resize(n); m2.resize(n); v1.resize(n); v2.resize(n);

        m1[0] = 1; m2[0] = 1;
        v1[0] = s[0]; v2[0] = s[0];

        rep(i, 1, n) {
            m1[i] = m1[i - 1] * p1;
            m2[i] = m2[i - 1] * p2;
            v1[i] = v1[i - 1] + m1[i] * s[i];
            v2[i] = v2[i - 1] + m2[i] * s[i];
        }
    }
    inline pair<mint1, mint2> hash(int l, int r) { // s[l..r]
        assert(l <= r); assert(r < n);
        mint1 a = v1[r];
        if (l) a -= v1[l - 1];
        a *= m1[n - 1 - r];

        mint2 b = v2[r];
        if (l) b -= v2[l - 1];
        b *= m2[n - 1 - r];

        return { a, b };
    }
    inline ll llhash(int l, int r) { // s[l..r]
        auto h = hash(l, r);
        return 1LL * h.first.get() * h.second.Mod + h.second.get();
    }
};




using vi = vector<int>;
int N;
int A[201010],B[201010];
int A2[201010],B2[201010];

void _main() {
    cin >> N;
    rep(i, 0, N)cin >> A[i];
    rep(i, 0, N)cin >> B[i];

    rep(i, 0, N)A2[i] = A[i] ^ A[(i + 1) % N];
    rep(i, 0, N)B2[i] = B[i] ^ B[(i + 1) % N];

    vector<int> v;
    rep(i, 0, N)v.push_back(A2[i]);
    rep(i, 0, N)v.push_back(A2[i]);
    rep(i, 0, N)v.push_back(B2[i]);

    RollingHash rh;
    rh.init(v);
    rep(k, 0, N)
    if (rh.hash(k, k + N-1) == rh.hash(N * 2, N * 2 + N-1)) {
        int x = A[k] ^B[0];
        cout<<k<<" "<<x<<endl;
    }
}