//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx")
//#undef LOCAL


#include <unistd.h>
#include <algorithm>
#include <array>
#include <cassert>
#include <cctype>
#include <cstring>
#include <sstream>
#include <string>
#include <type_traits>
#include <vector>


namespace yosupo {

namespace internal {

int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

}  // namespace internal

int bsf(unsigned int n) { return __builtin_ctz(n); }
int bsf(unsigned long n) { return __builtin_ctzl(n); }
int bsf(unsigned long long n) { return __builtin_ctzll(n); }
int bsf(unsigned __int128 n) {
    unsigned long long low = (unsigned long long)(n);
    unsigned long long high = (unsigned long long)(n >> 64);
    return low ? __builtin_ctzll(low) : 64 + __builtin_ctzll(high);
}

int bsr(unsigned int n) {
    return 8 * (int)sizeof(unsigned int) - 1 - __builtin_clz(n);
}
int bsr(unsigned long n) {
    return 8 * (int)sizeof(unsigned long) - 1 - __builtin_clzl(n);
}
int bsr(unsigned long long n) {
    return 8 * (int)sizeof(unsigned long long) - 1 - __builtin_clzll(n);
}
int bsr(unsigned __int128 n) {
    unsigned long long low = (unsigned long long)(n);
    unsigned long long high = (unsigned long long)(n >> 64);
    return high ? 127 - __builtin_clzll(high) : 63 - __builtin_ctzll(low);
}

int popcnt(unsigned int n) { return __builtin_popcount(n); }
int popcnt(unsigned long n) { return __builtin_popcountl(n); }
int popcnt(unsigned long long n) { return __builtin_popcountll(n); }

}  // namespace yosupo

#include <cassert>
#include <numeric>
#include <type_traits>

namespace yosupo {

namespace internal {

template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value ||
                                  internal::is_signed_int128<T>::value ||
                                  internal::is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

template <class T>
using is_integral_t = std::enable_if_t<is_integral<T>::value>;

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace yosupo

namespace yosupo {

struct Scanner {
  public:
    Scanner(const Scanner&) = delete;
    Scanner& operator=(const Scanner&) = delete;

    Scanner(FILE* fp) : fd(fileno(fp)) { line[0] = 127; }

    void read() {}
    template <class H, class... T> void read(H& h, T&... t) {
        bool f = read_single(h);
        assert(f);
        read(t...);
    }

    int read_unsafe() { return 0; }
    template <class H, class... T> int read_unsafe(H& h, T&... t) {
        bool f = read_single(h);
        if (!f) return 0;
        return 1 + read_unsafe(t...);
    }

    int close() { return ::close(fd); }

  private:
    static constexpr int SIZE = 1 << 15;

    int fd = -1;
    std::array<char, SIZE + 1> line;
    int st = 0, ed = 0;
    bool eof = false;

    bool read_single(std::string& ref) {
        if (!skip_space()) return false;
        ref = "";
        while (true) {
            char c = top();
            if (c <= ' ') break;
            ref += c;
            st++;
        }
        return true;
    }
    bool read_single(double& ref) {
        std::string s;
        if (!read_single(s)) return false;
        ref = std::stod(s);
        return true;
    }

    template <class T,
              std::enable_if_t<std::is_same<T, char>::value>* = nullptr>
    bool read_single(T& ref) {
        if (!skip_space<50>()) return false;
        ref = top();
        st++;
        return true;
    }

    template <class T,
              internal::is_signed_int_t<T>* = nullptr,
              std::enable_if_t<!std::is_same<T, char>::value>* = nullptr>
    bool read_single(T& sref) {
        using U = internal::to_unsigned_t<T>;
        if (!skip_space<50>()) return false;
        bool neg = false;
        if (line[st] == '-') {
            neg = true;
            st++;
        }
        U ref = 0;
        do {
            ref = 10 * ref + (line[st++] & 0x0f);
        } while (line[st] >= '0');
        sref = neg ? -ref : ref;
        return true;
    }
    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<!std::is_same<U, char>::value>* = nullptr>
    bool read_single(U& ref) {
        if (!skip_space<50>()) return false;
        ref = 0;
        do {
            ref = 10 * ref + (line[st++] & 0x0f);
        } while (line[st] >= '0');
        return true;
    }

    bool reread() {
        if (ed - st >= 50) return true;
        if (st > SIZE / 2) {
            std::memmove(line.data(), line.data() + st, ed - st);
            ed -= st;
            st = 0;
        }
        if (eof) return false;
        auto u = ::read(fd, line.data() + ed, SIZE - ed);
        if (u == 0) {
            eof = true;
            line[ed] = '\0';
            u = 1;
        }
        ed += int(u);
        line[ed] = char(127);
        return true;
    }

    char top() {
        if (st == ed) {
            bool f = reread();
            assert(f);
        }
        return line[st];
    }

    template <int TOKEN_LEN = 0> bool skip_space() {
        while (true) {
            while (line[st] <= ' ') st++;
            if (ed - st > TOKEN_LEN) return true;
            if (st > ed) st = ed;
            for (auto i = st; i < ed; i++) {
                if (line[i] <= ' ') return true;
            }
            if (!reread()) return false;
        }
    }
};

struct Printer {
  public:
    template <char sep = ' ', bool F = false> void write() {}
    template <char sep = ' ', bool F = false, class H, class... T>
    void write(const H& h, const T&... t) {
        if (F) write_single(sep);
        write_single(h);
        write<true>(t...);
    }
    template <char sep = ' ', class... T> void writeln(const T&... t) {
        write<sep>(t...);
        write_single('\n');
    }

    Printer(FILE* _fp) : fd(fileno(_fp)) {}
    ~Printer() { flush(); }

    int close() {
        flush();
        return ::close(fd);
    }

    void flush() {
        if (pos) {
            auto res = ::write(fd, line.data(), pos);
            assert(res != -1);
            pos = 0;
        }
    }

  private:
    static std::array<std::array<char, 2>, 100> small;
    static std::array<unsigned long long, 20> tens;

    static constexpr size_t SIZE = 1 << 15;
    int fd;
    std::array<char, SIZE> line;
    size_t pos = 0;
    std::stringstream ss;

    template <class T,
              std::enable_if_t<std::is_same<char, T>::value>* = nullptr>
    void write_single(const T& val) {
        if (pos == SIZE) flush();
        line[pos++] = val;
    }

    template <class T,
              internal::is_signed_int_t<T>* = nullptr,
              std::enable_if_t<!std::is_same<char, T>::value>* = nullptr>
    void write_single(const T& val) {
        using U = internal::to_unsigned_t<T>;
        if (val == 0) {
            write_single('0');
            return;
        }
        if (pos > SIZE - 50) flush();
        U uval = val;
        if (val < 0) {
            write_single('-');
            uval = -uval;
        }
        write_unsigned(uval);
    }

    template <class U, internal::is_unsigned_int_t<U>* = nullptr>
    void write_single(U uval) {
        if (uval == 0) {
            write_single('0');
            return;
        }
        if (pos > SIZE - 50) flush();

        write_unsigned(uval);
    }

    template <class U, internal::is_unsigned_int_t<U>* = nullptr>
    static int calc_len(U x) {
        int i = (bsr(x) * 3 + 3) / 10;
        if (x < tens[i])
            return i;
        else
            return i + 1;
    }

    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<2 >= sizeof(U)>* = nullptr>
    void write_unsigned(U uval) {
        size_t len = calc_len(uval);
        pos += len;

        char* ptr = line.data() + pos;
        while (uval >= 100) {
            ptr -= 2;
            memcpy(ptr, small[uval % 100].data(), 2);
            uval /= 100;
        }
        if (uval >= 10) {
            memcpy(ptr - 2, small[uval].data(), 2);
        } else {
            *(ptr - 1) = char('0' + uval);
        }
    }

    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<4 == sizeof(U)>* = nullptr>
    void write_unsigned(U uval) {
        std::array<char, 8> buf;
        memcpy(buf.data() + 6, small[uval % 100].data(), 2);
        memcpy(buf.data() + 4, small[uval / 100 % 100].data(), 2);
        memcpy(buf.data() + 2, small[uval / 10000 % 100].data(), 2);
        memcpy(buf.data() + 0, small[uval / 1000000 % 100].data(), 2);

        if (uval >= 100000000) {
            if (uval >= 1000000000) {
                memcpy(line.data() + pos, small[uval / 100000000 % 100].data(),
                       2);
                pos += 2;
            } else {
                line[pos] = char('0' + uval / 100000000);
                pos++;
            }
            memcpy(line.data() + pos, buf.data(), 8);
            pos += 8;
        } else {
            size_t len = calc_len(uval);
            memcpy(line.data() + pos, buf.data() + (8 - len), len);
            pos += len;
        }
    }

    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<8 == sizeof(U)>* = nullptr>
    void write_unsigned(U uval) {
        size_t len = calc_len(uval);
        pos += len;

        char* ptr = line.data() + pos;
        while (uval >= 100) {
            ptr -= 2;
            memcpy(ptr, small[uval % 100].data(), 2);
            uval /= 100;
        }
        if (uval >= 10) {
            memcpy(ptr - 2, small[uval].data(), 2);
        } else {
            *(ptr - 1) = char('0' + uval);
        }
    }

    template <
        class U,
        std::enable_if_t<internal::is_unsigned_int128<U>::value>* = nullptr>
    void write_unsigned(U uval) {
        static std::array<char, 50> buf;
        size_t len = 0;
        while (uval > 0) {
            buf[len++] = char((uval % 10) + '0');
            uval /= 10;
        }
        std::reverse(buf.begin(), buf.begin() + len);
        memcpy(line.data() + pos, buf.data(), len);
        pos += len;
    }

    void write_single(const std::string& s) {
        for (char c : s) write_single(c);
    }
    void write_single(const char* s) {
        size_t len = strlen(s);
        for (size_t i = 0; i < len; i++) write_single(s[i]);
    }
    template <class T> void write_single(const std::vector<T>& val) {
        auto n = val.size();
        for (size_t i = 0; i < n; i++) {
            if (i) write_single(' ');
            write_single(val[i]);
        }
    }
};

std::array<std::array<char, 2>, 100> Printer::small = [] {
    std::array<std::array<char, 2>, 100> table;
    for (int i = 0; i <= 99; i++) {
        table[i][1] = char('0' + (i % 10));
        table[i][0] = char('0' + (i / 10 % 10));
    }
    return table;
}();
std::array<unsigned long long, 20> Printer::tens = [] {
    std::array<unsigned long long, 20> table;
    for (int i = 0; i < 20; i++) {
        table[i] = 1;
        for (int j = 0; j < i; j++) {
            table[i] *= 10;
        }
    }
    return table;
}();

}  // namespace yosupo

#include <array>
#include <cassert>
#include <chrono>
#include <cstdint>
#include <type_traits>


namespace yosupo {

struct Xoshiro256StarStar {
  public:
    using result_type = uint64_t;
    Xoshiro256StarStar() : Xoshiro256StarStar(0) {}
    explicit Xoshiro256StarStar(uint64_t seed) {
        for (int i = 0; i < 4; i++) {
            uint64_t z = (seed += 0x9e3779b97f4a7c15);
            z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
            z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
            s[i] = z ^ (z >> 31);
        }
    }

    static constexpr result_type min() { return 0; }
    static constexpr result_type max() { return -1; }

    result_type operator()() {
        const uint64_t result_starstar = rotl(s[1] * 5, 7) * 9;

        const uint64_t t = s[1] << 17;

        s[2] ^= s[0];
        s[3] ^= s[1];
        s[1] ^= s[2];
        s[0] ^= s[3];

        s[2] ^= t;

        s[3] = rotl(s[3], 45);

        return result_starstar;
    }

  private:
    static uint64_t rotl(const uint64_t x, int k) {
        return (x << k) | (x >> (64 - k));
    }

    std::array<uint64_t, 4> s;
};

namespace internal {

template <class G> uint64_t uniform(uint64_t upper, G& gen) {
    static_assert(std::is_same<uint64_t, typename G::result_type>::value, "");
    static_assert(G::min() == 0, "");
    static_assert(G::max() == uint64_t(-1), "");
    if (!(upper & (upper + 1))) {
        return gen() & upper;
    }
    int log = bsr(upper);
    uint64_t mask = (log == 63) ? ~0ULL : (1ULL << (log + 1)) - 1;
    while (true) {
        uint64_t r = gen() & mask;
        if (r <= upper) return r;
    }
}

}  // namespace internal

Xoshiro256StarStar& global_gen() {
    static Xoshiro256StarStar gen(
        std::chrono::steady_clock::now().time_since_epoch().count());
    return gen;
}

template <class T, class G> T uniform(T lower, T upper, G& gen) {
    return T(lower + internal::uniform(uint64_t(upper) - uint64_t(lower), gen));
}
template <class T> T uniform(T lower, T upper) {
    return uniform(lower, upper, global_gen());
}

template <class G> bool uniform_bool(G& gen) {
    return internal::uniform(1, gen) == 1;
}
bool uniform_bool() { return uniform_bool(global_gen()); }

template <class T, class G>
std::pair<T, T> uniform_pair(T lower, T upper, G& gen) {
    assert(upper - lower >= 1);
    T a, b;
    do {
        a = uniform(lower, upper, gen);
        b = uniform(lower, upper, gen);
    } while (a == b);
    if (a > b) std::swap(a, b);
    return {a, b};
}
template <class T> std::pair<T, T> uniform_pair(T lower, T upper) {
    return uniform_pair(lower, upper, global_gen());
}

}  // namespace yosupo
using namespace yosupo;

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <complex>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>

using namespace std;

using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;

#ifdef LOCAL

ostream& operator<<(ostream& os, __int128_t x) {
    if (x < 0) {
        os << "-";
        x *= -1;
    }
    if (x == 0) {
        return os << "0";
    }
    string s;
    while (x) {
        s += char(x % 10 + '0');
        x /= 10;
    }
    reverse(s.begin(), s.end());
    return os << s;
}
ostream& operator<<(ostream& os, __uint128_t x) {
    if (x == 0) {
        return os << "0";
    }
    string s;
    while (x) {
        s += char(x % 10 + '0');
        x /= 10;
    }
    reverse(s.begin(), s.end());
    return os << s;
}

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p);
template <class T> ostream& operator<<(ostream& os, const V<T>& v);
template <class T> ostream& operator<<(ostream& os, const deque<T>& v);
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T> ostream& operator<<(ostream& os, const set<T>& s);
template <class T, class U>
ostream& operator<<(ostream& os, const map<T, U>& m);

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    return os << "P(" << p.first << ", " << p.second << ")";
}

template <class T> ostream& operator<<(ostream& os, const V<T>& v) {
    os << "[";
    bool f = false;
    for (auto d : v) {
        if (f) os << ", ";
        f = true;
        os << d;
    }
    return os << "]";
}

template <class T> ostream& operator<<(ostream& os, const deque<T>& v) {
    os << "[";
    bool f = false;
    for (auto d : v) {
        if (f) os << ", ";
        f = true;
        os << d;
    }
    return os << "]";
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
    os << "[";
    bool f = false;
    for (auto d : a) {
        if (f) os << ", ";
        f = true;
        os << d;
    }
    return os << "]";
}

template <class T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << "{";
    bool f = false;
    for (auto d : s) {
        if (f) os << ", ";
        f = true;
        os << d;
    }
    return os << "}";
}
template <class T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << "{";
    bool f = false;
    for (auto d : s) {
        if (f) os << ", ";
        f = true;
        os << d;
    }
    return os << "}";
}

template <class T, class U>
ostream& operator<<(ostream& os, const map<T, U>& s) {
    os << "{";
    bool f = false;
    for (auto p : s) {
        if (f) os << ", ";
        f = true;
        os << p.first << ": " << p.second;
    }
    return os << "}";
}

struct PrettyOS {
    ostream& os;
    bool first;

    template <class T> auto operator<<(T&& x) {
        if (!first) os << ", ";
        first = false;
        os << x;
        return *this;
    }
};
template <class... T> void dbg0(T&&... t) {
    (PrettyOS{cerr, true} << ... << t);
}
#define dbg(...)                                            \
    do {                                                    \
        cerr << __LINE__ << " : " << #__VA_ARGS__ << " = "; \
        dbg0(__VA_ARGS__);                                  \
        cerr << endl;                                       \
    } while (false);
#else
#define dbg(...)
#endif

struct Nimber64;
Nimber64 mul_naive(Nimber64 l, Nimber64 r);
struct Nimber64 {
    const static V<ull> factor;
    const static array<array<unsigned char, 256>, 256> small;
    const static array<array<array<Nimber64, 256>, 8>, 8> precalc;
    ull v;
    Nimber64() : v(0) {}
    Nimber64(ull _v) : v(_v) {}
    const Nimber64 operator+(Nimber64 r) const { return v ^ r.v; }
    const Nimber64 operator-(Nimber64 r) const { return v ^ r.v; }
    const Nimber64 operator*(Nimber64 r) const {
        Nimber64 ans;
        for (int i = 0; i < 8; i++) {
            for (int j = 0; j < 8; j++) {
                ull x = (v >> (8 * i)) % 256;
                ull y = (r.v >> (8 * j)) % 256;
                ans += precalc[i][j][small[x][y]];
            }
        }
        return ans;
    }
    const Nimber64 operator/(Nimber64 r) const {
        auto ri = r.pow(ull(-1) - 1);
        assert((r * ri) == Nimber64(1));
        return (*this) * ri;
    }
    bool operator==(Nimber64 r) const { return v == r.v; }
    bool operator!=(Nimber64 r) const { return v != r.v; }
    Nimber64& operator+=(Nimber64 r) { return *this = *this + r; }
    Nimber64& operator-=(Nimber64 r) { return *this = *this - r; }
    Nimber64& operator*=(Nimber64 r) { return *this = *this * r; }
    Nimber64& operator/=(Nimber64 r) { return *this = *this / r; }

    Nimber64 pow(ull n) const {
        Nimber64 x = *this, r = 1;
        while (n) {
            if (n & 1) r = r * x;
            x = x * x;
            n >>= 1;
        }
        return r;
    }

    ull discrete_logarithm(Nimber64 y) {
        ull rem = 0, mod = 1;
        for (ull p : factor) {
            ull STEP = 1;
            while (4 * STEP * STEP < p) STEP *= 2;
            auto inside = [&](Nimber64 x, Nimber64 z) {
                unordered_map<ull, int> mp;
                Nimber64 big = 1;  // x^m
                for (int i = 0; i < int(STEP); i++) {
                    mp[z.v] = i;
                    z *= x;
                    big *= x;
                }
                Nimber64 now = 1;
                for (ull step = 0; step < ull(p + 10); step += STEP) {
                    now *= big;
                    // check [step + 1, step + STEP]
                    if (mp.find(now.v) != mp.end()) {
                        return (step + STEP) - mp[now.v];
                    }
                }
                return ull(-1);
            };

            ull q = ull(-1) / p;
            ull res = inside((*this).pow(q), y.pow(q));
            if (res == ull(-1)) {
                return ull(-1);
            }
            res %= p;
            // mod p = v
            if (mod == 1) {
                rem = res;
                mod = p;
            } else {
                while (rem % p != res) rem += mod;
                mod *= p;
            }
        }
        return rem;
    }

    bool is_primitive_root() const {
        for (ull p : factor) {
            if ((*this).pow(ull(-1) / p).v == 1) return false;
        }
        return true;
    }
};
const V<ull> Nimber64::factor = {
    6700417, 65537, 641, 257, 17, 5, 3,
};

Nimber64 mul_naive(Nimber64 l, Nimber64 r) {
    ull a = l.v, b = r.v;
    if (a < b) swap(a, b);
    if (b == 0) return 0;
    if (b == 1) return a;
    int p = 32;
    while (max(a, b) < (1ULL << p)) p /= 2;
    ull power = 1ULL << p;
    if (a >= power && b >= power) {
        Nimber64 ans;
        ans += mul_naive(a % power, b % power);
        ans += mul_naive(a / power, b % power).v * power;
        ans += mul_naive(a % power, b / power).v * power;
        auto x = mul_naive(a / power, b / power);
        ans += x.v * power;
        ans += mul_naive(x.v, power / 2);
        return ans;
    } else {
        return Nimber64(mul_naive(a / power, b).v * power) +
               mul_naive(a % power, b);
    }
};

const array<array<unsigned char, 256>, 256> Nimber64::small = []() {
    array<array<unsigned char, 256>, 256> small;
    for (int i = 0; i < 256; i++) {
        for (int j = 0; j < 256; j++) {
            small[i][j] = (unsigned char)(mul_naive(i, j).v);
        }
    }
    return small;
}();

const array<array<array<Nimber64, 256>, 8>, 8> Nimber64::precalc = []() {
    array<array<array<Nimber64, 256>, 8>, 8> precalc;
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            for (int k = 0; k < 256; k++) {
                precalc[i][j][k] =
                    mul_naive(mul_naive(1ULL << (8 * i), 1ULL << (8 * j)), k);
            }
        }
    }
    return precalc;
}();

struct Nimber32 {
    const static V<uint> factor;
    uint v;
    Nimber32() : v(0) {}
    Nimber32(uint _v) : v(_v) {}
    const Nimber32 operator+(Nimber32 r) const { return v ^ r.v; }
    const Nimber32 operator-(Nimber32 r) const { return v ^ r.v; }
    const Nimber32 operator*(Nimber32 r) const {
        Nimber32 ans;
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < 4; j++) {
                uint x = (v >> (8 * i)) % 256;
                uint y = (r.v >> (8 * j)) % 256;
                ans += uint(Nimber64::precalc[i][j][Nimber64::small[x][y]].v);
            }
        }
        return ans;
    }
    bool operator==(Nimber32 r) const { return v == r.v; }
    bool operator!=(Nimber32 r) const { return v != r.v; }
    Nimber32& operator+=(Nimber32 r) { return *this = *this + r; }
    Nimber32& operator-=(Nimber32 r) { return *this = *this - r; }
    Nimber32& operator*=(Nimber32 r) { return *this = *this * r; }
};

struct Nimber16 {
    const static V<uint> factor;
    ushort v;
    Nimber16() : v(0) {}
    Nimber16(ushort _v) : v(_v) {}
    const Nimber16 operator+(Nimber16 r) const { return v ^ r.v; }
    const Nimber16 operator-(Nimber16 r) const { return v ^ r.v; }
    const Nimber16 operator*(Nimber16 r) const {
        Nimber16 ans;
        for (int i = 0; i < 2; i++) {
            for (int j = 0; j < 2; j++) {
                uint x = (v >> (8 * i)) % 256;
                uint y = (r.v >> (8 * j)) % 256;
                ans += ushort(Nimber64::precalc[i][j][Nimber64::small[x][y]].v);
            }
        }
        return ans;
    }
    bool operator==(Nimber16 r) const { return v == r.v; }
    bool operator!=(Nimber16 r) const { return v != r.v; }
    Nimber16& operator+=(Nimber16 r) { return *this = *this + r; }
    Nimber16& operator-=(Nimber16 r) { return *this = *this - r; }
    Nimber16& operator*=(Nimber16 r) { return *this = *this * r; }
};

Scanner sc = Scanner(stdin);
Printer pr = Printer(stdout);

int naive(VV<bool> mp, int x, int y, int z) {
    int n = int(mp.size());
    V<int> idx(n);
    iota(idx.begin(), idx.end(), 0);

    int ans = n + 1;
    do {
        bool f0 = false, f1 = false, f2 = false;
        for (int i = 0; i < n; i++) {
            if (i && !mp[idx[i - 1]][idx[i]]) break;
            if (idx[i] == x) f0 = true;
            if (idx[i] == y) f1 = true;
            if (idx[i] == z) f2 = true;

            if (mp[idx[i]][idx[0]] && f0 && f1 && f2) {
                ans = min(ans, i + 1);
            }
        }
    } while (next_permutation(idx.begin(), idx.end()));

    if (ans == n + 1) ans = -1;
    return ans;
}

V<int> naive_path(VV<bool> mp, int x, int y, int z) {
    int n = int(mp.size());
    V<int> idx(n);
    iota(idx.begin(), idx.end(), 0);

    V<int> ans;
    do {
        if (idx[0] != x) continue;
        bool f0 = false, f1 = false, f2 = false;
        for (int i = 0; i < n; i++) {
            if (i && !mp[idx[i - 1]][idx[i]]) break;
            if (idx[i] == x) f0 = true;
            if (idx[i] == y) f1 = true;
            if (idx[i] == z) f2 = true;

            if (mp[idx[i]][idx[0]] && f0 && f1 && f2) {
                V<int> cur = {idx.begin(), idx.begin() + i + 1};
                cur.push_back(idx[0]);
                if (ans.empty() || cur.size() < ans.size() || (cur.size() == ans.size() && cur < ans)) {
                    ans = cur;
                }
            }
        }
    } while (next_permutation(idx.begin(), idx.end()));

    return ans;
}


/*
- 始点s, 終点t, mid上の頂点をすべてちょうど一度ずつ通るパスを探索
- 無向グラフ, midはdistinctで間に辺が無いことを仮定
- return pair(パスの長さの最小 or 1, 最短パスのうち、sの次に訪れうる最小の頂点番号)
*/
pair<int, int> find_path(const VV<int>& g, int s, int t, V<int> mid) {
/*    dbg(s, t, mid);
    for (auto v : g) {
        dbg(v);
    }*/
    using T = Nimber16;

    int n = int(g.size());
    int k = int(mid.size());

    V<int> is_mid(n, -1);
    for (int i = 0; i < k; i++) {
        is_mid[mid[i]] = i;
    }

    VV<T> val(n, V<T>(n));
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            val[i][j] = val[j][i] = uniform<ushort>(0, -1);
        }
    }

    V<VV<T>> dp(1 << k, VV<T>(n + 1, V<T>(n)));

    /*
    dp[f][len][p]:

    次の条件を満たすwalkを列挙、sum prod_{e in path} val[{e}]
    - tは最初のみに出てくる, sは出てこない
    - midは高々1度ずつ出てくる、fはmidが出現したかのbitmap
    - walk: (t -> ... -> p)
    - walkはmidを中点とする折返し(a -> (mid vertex) -> a)を含まない

    F_{2^p}ならサイクルがキャンセリングされる。最初から見ていき、初めて2度出てきた頂点ペアの間を反転する。

    dp[true][true][i][x][*][x] != 0ならば答えi
    */

    dp[0][0][t] += 1;
    for (int len = 0; len < n; len++) {
        int ans = n;
        for (int f = 0; f < (1 << k); f++) {
            VV<T> dp2(k, V<T>(n));
            for (int p = 0; p < n; p++) {
                if (dp[f][len][p] == T(0)) continue;
                assert(is_mid[p] == -1);

                for (int q : g[p]) {
                    if (q == t) continue;
                    if (q == s) {
                        if (f == ((1 << k) - 1)) {
                            ans = min(ans, p);
                            //return {len + k + 1, p};
                        }
                        continue;
                    }

                    T v = dp[f][len][p] * val[p][q];

                    if (is_mid[q] != -1) {
                        dp2[is_mid[q]][p] += v;;
                        continue;
                    }
                    dp[f][len + 1][q] += v;
                }
            }
            for (int i = 0; i < k; i++) {
                if (f & (1 << i)) continue;
                int p = mid[i];
                T sum = 0;
                for (auto x : dp2[i]) sum += x;
                for (int q : g[p]) {
                    if (q == t) continue;
                    T v = (sum - dp2[i][q]) * val[p][q];
                    if (v == T(0)) continue;

                    if (q == s) {
                        if ((f | (1 << i)) == ((1 << k) - 1)) {
                            ans = min(ans, p);
                        }
                        continue;
                    }         
                    dp[f | (1 << i)][len + 1][q] += v;
                }
            }
        }
        if (ans < n) {
            return {len + k + 1, ans};
        }
    }

    return {-1, 0};
}
pair<int, int> find_path_rec(const VV<int>& g, int s, int t, V<int> mid, int times=2) {
    pair<int, int> ans = {TEN(9), 0};
    for (int i = 0; i < times; i++) {
        auto cans = find_path(g, s, t, mid);
        if (cans.first != -1) ans = min(ans, cans);
    }
    if (ans.first == TEN(9)) ans.first = -1;
    return ans;
}   

/*
int solve(VV<bool> mp, int x, int y, int z) {
    int n = int(mp.size());
    // duplicate x
    VV<bool> mp2(n + 1, V<bool>(n + 1));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            mp2[i][j] = mp[i][j];
        }
    }
    for (int i = 0; i < n; i++) {
        mp2[i][n] = mp2[n][i] = mp2[x][i];
    }

    auto result = find_path(mp2, x, n, {y, z});
    return result.first;
}
*/
V<int> solve_path(VV<bool> g, int x, int y, int z) {
    auto cg = [&]() {
        int n = int(g.size());
        VV<int> g2(g.size());
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (g[i][j]) {
                    g2[i].push_back(j);
                }
            }
        }
        return g2;
    };
    int n = int(g.size());
    {
        // duplicate x
        VV<bool> g2(n + 1, V<bool>(n + 1));
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                g2[i][j] = g[i][j];
            }
        }
        for (int i = 0; i < n; i++) {
            g2[i][n] = g2[n][i] = g[x][i];
        }
        g = g2;
        n++;
    }

    // x -> ... -> y -> ... -> z -> ... -> (n - 1)

    if (find_path_rec(cg(), x, n - 1, {y, z}).first == -1) return {};

    V<int> idx(n), ridx(n);
    iota(idx.begin(), idx.end(), 0);
    iota(ridx.begin(), ridx.end(), 0);

    V<int> answer;
    answer.push_back(x);
    int s = x;
    while (s != n - 1) {
        V<int> mid;
        if (y != s && idx[y] != -1) mid.push_back(idx[y]);
        if (z != s && idx[z] != -1) mid.push_back(idx[z]);
        auto result = find_path_rec(cg(), idx[s], idx[n - 1], mid);
//        dbg(result);
        assert(result.first != -1);
        int s2 = ridx[result.second];
        answer.push_back(s2);

        // remove s
        {
            V<int> idx2 = idx;
            int m = 0;
            for (int i = 0; i < n; i++) {
                if (idx2[i] > idx2[s]) idx2[i]--;
                m = max(m, idx2[i] + 1);
            }
            idx2[s] = -1;
            V<int> ridx2(n, -1);
            for (int i = 0; i < n; i++) {
                if (idx2[i] != -1) ridx2[idx2[i]] = i;
            }

            VV<bool> g2(m, V<bool>(m));
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < m; j++) {
                    g2[i][j] = g[idx[ridx2[i]]][idx[ridx2[j]]];
                }
            }
            idx = idx2;
            ridx = ridx2;
            g = g2;
        }
        s = s2;
    }
    answer.back() = x;
    return answer;
}

int main() {
    int n, m;
    sc.read(n, m);
    VV<bool> mp(n, V<bool>(n, true));
    for (int i = 0; i < n; i++) {
        mp[i][i] = false;
    }
    int x, y, z;
    sc.read(x, y, z);
    x--; y--; z--;
    for (int i = 0; i < m; i++) {
        int a, b;
        sc.read(a, b);
        a--; b--;
        mp[a][b] = mp[b][a] = false;
    }

//    auto expect = solve2(mp, x, y, z);
    auto answer = solve_path(mp, x, y, z);
    dbg(answer);
//    dbg(answer, expect);
//    pr.writeln(answer);


    if (answer.empty()) {
        pr.writeln(-1);
        return 0;
    }
    int len = int(answer.size() - 1);
    pr.writeln(len);
    for (int i = 0; i <= len; i++) {
        pr.write(answer[i] + 1);
        if (i != len) pr.write(' ');
    }
    pr.writeln();

/*
    while (true) {
        int n = uniform(3, 10);
        VV<bool> mp(n, V<bool>(n, true));
        for (int i = 0; i < n; i++) {
            mp[i][i] = false;
        }

        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                if (uniform(0, 10) >= 5) {
                    mp[i][j] = mp[j][i] = false;
                }
            }
        }
//        mp[0][1] = mp[1][0] = false;
//        mp[2][0] = mp[0][2] = false;

        mp[1][2] = mp[2][1] = false;

        auto expect = naive_path(mp, 0, 1, 2);
        auto actual = solve_path(mp, 0, 1, 2);

        if (expect != actual) {
            dbg(n);
            for (auto v : mp) {
                dbg(v);
            }
            dbg(expect, actual);
            assert(false);
        }
    }*/
    return 0;
}