/** * date : 2021-12-06 23:02:06 */ #define NDEBUG using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; T &x() { return first; } const T &x() const { return first; } U &y() { return second; } const U &y() const { return second; } P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } P operator*(int r) const { return {first * r, second * r}; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &... u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &... u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &... u) { cout << t; outr(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug namespace DebugImpl { template struct is_specialize : false_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } template ::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template void dump(const T& t, enable_if_t::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template void dump(const pair&); template void dump(const pair&); template void dump(const T& t, enable_if_t::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template void dump(const pair& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template void dump(const pair& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif // macro #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // template struct edge { int src, to; T cost; edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {} edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {} edge &operator=(const int &x) { to = x; return *this; } operator int() const { return to; } }; template using Edges = vector>; template using WeightedGraph = vector>; using UnweightedGraph = vector>; // Input of (Unweighted) Graph UnweightedGraph graph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { UnweightedGraph g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; if (is_1origin) x--, y--; g[x].push_back(y); if (!is_directed) g[y].push_back(x); } return g; } // Input of Weighted Graph template WeightedGraph wgraph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { WeightedGraph g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; cin >> c; if (is_1origin) x--, y--; g[x].emplace_back(x, y, c); if (!is_directed) g[y].emplace_back(y, x, c); } return g; } // Input of Edges template Edges esgraph(int N, int M, int is_weighted = true, bool is_1origin = true) { Edges es; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; es.emplace_back(x, y, c); } return es; } // Input of Adjacency Matrix template vector> adjgraph(int N, int M, T INF, int is_weighted = true, bool is_directed = false, bool is_1origin = true) { vector> d(N, vector(N, INF)); for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; d[x][y] = c; if (!is_directed) d[y][x] = c; } return d; } namespace my_rand { // [0, 2^64 - 1) uint64_t rng() { static uint64_t x_ = uint64_t(chrono::duration_cast( chrono::high_resolution_clock::now().time_since_epoch()) .count()) * 10150724397891781847ULL; x_ ^= x_ << 7; return x_ ^= x_ >> 9; } // [l, r) int64_t randint(int64_t l, int64_t r) { assert(l < r); return l + rng() % (r - l); } // choose n numbers from [l, r) without overlapping vector randset(int64_t l, int64_t r, int64_t n) { assert(l <= r && n <= r - l); unordered_set s; for (int64_t i = n; i; --i) { int64_t m = randint(l, r + 1 - i); if (s.find(m) != s.end()) m = r - i; s.insert(m); } vector ret; for (auto& x : s) ret.push_back(x); return ret; } // [0.0, 1.0) double rnd() { union raw_cast { double t; uint64_t u; }; constexpr uint64_t p = uint64_t(1023 - 64) << 52; return rng() * ((raw_cast*)(&p))->t; } template void randshf(vector& v) { int n = v.size(); for (int loop = 0; loop < 2; loop++) for (int i = 0; i < n; i++) swap(v[i], v[randint(0, n)]); } } // namespace my_rand using my_rand::randint; using my_rand::randset; using my_rand::randshf; using my_rand::rnd; using my_rand::rng; struct Timer { chrono::high_resolution_clock::time_point st; Timer() { reset(); } void reset() { st = chrono::high_resolution_clock::now(); } chrono::milliseconds::rep elapsed() { auto ed = chrono::high_resolution_clock::now(); return chrono::duration_cast(ed - st).count(); } }; using namespace Nyaan; using ull = uint64_t; // http://yosupo06.github.io/Algorithm/src/nimber.test.cpp struct Nimber64; Nimber64 mul_naive(Nimber64 l, Nimber64 r); struct Nimber64 { const static V factor; const static array, 256> small; const static array, 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 { 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; } 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 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 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 (int step = 0; step < int(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 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, 256> Nimber64::small = []() { array, 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, 8>, 8> Nimber64::precalc = []() { array, 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; }(); u64 nim_product(u64 a, u64 b) { return (Nimber64(a) * Nimber64(b)).v; } // y 訪問済み / z 訪問済み / 今のマス / 前のマス u64 dp[2][2][128][128]; u64 nx[2][2][128][128]; void Nyaan::solve() { Timer timer; inl(N, M, X, Y, Z); --X, --Y, --Z; vvl g(N, vl(N)); rep(i, M) { inl(u, v); --u, --v; g[u][v] = g[v][u] = 1; } Edges es; rep(i, N) rep(j, i) { if (g[i][j] == 1) continue; u64 x = rng() % u64(-1) + 1; es.emplace_back(i, j, x); /* if (i == X or j == X) { x = rng() % u64(-1) + 1; } */ es.emplace_back(j, i, x); } sort(all(es), [](edge& u, edge& v) { if (u.src != v.src) return u.src < v.src; return u.to < v.to; }); // y 訪問済み / z 訪問済み / 今のマス / 前のマス dp[0][0][X][X] = 1; rep1(L, N) { //if (timer.elapsed() > 7000) exit(1); memset(nx, 0, sizeof(nx)); rep(ky, 2) rep(kz, 2) { each(e, es) { int c = e.src; int d = e.to; u64 w = e.cost; if(ky == 1 and d == Y) continue; if(kz == 1 and d == Z) continue; int nky = ky | (d == Y); int nkz = kz | (d == Z); rep(p, N) { if (p == d) continue; if (dp[ky][kz][c][p] == 0) continue; nx[nky][nkz][d][c] ^= nim_product(dp[ky][kz][c][p], w); } } } swap(dp, nx); /* reg(ky, 1, 2) reg(kz, 1, 2) rep(c, N) rep(d, N) { if (dp[ky][kz][c][d] != 0) trc(L, ky, kz, c + 1, d + 1, dp[ky][kz][c][d]); } */ rep(i, N) if (dp[1][1][X][i] != u64{}) die(L); } die(-1); }