/** * date : 2021-12-21 22:40:50 */ #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(); } // namespace NimberImpl { using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; struct calc8 { u16 dp[1 << 8][1 << 8]; constexpr calc8() : dp() { dp[0][0] = dp[0][1] = dp[1][0] = 0; dp[1][1] = 1; for (int e = 1; e <= 3; e++) { int p = 1 << e, q = p >> 1; u16 ep = 1u << p, eq = 1u << q; for (u16 i = 0; i < ep; i++) { for (u16 j = i; j < ep; j++) { if (i < eq && j < eq) continue; if (min(i, j) <= 1u) { dp[i][j] = dp[j][i] = i * j; continue; } u16 iu = i >> q, il = i & (eq - 1); u16 ju = j >> q, jl = j & (eq - 1); u16 u = dp[iu][ju], l = dp[il][jl]; u16 ul = dp[iu ^ il][ju ^ jl]; u16 uq = dp[u][eq >> 1]; dp[i][j] = ((ul ^ l) << q) ^ uq ^ l; dp[j][i] = dp[i][j]; } } } } } constexpr c8; struct calc16 { private: static constexpr u16 proot = 10279; static constexpr u32 ppoly = 92191; static constexpr int order = 65535; u16 base[16], exp[(1 << 18) + 100]; int log[1 << 16]; constexpr u16 d(u32 x) { return (x << 1) ^ (x < 32768u ? 0 : ppoly); } constexpr u16 naive(u16 i, u16 j) { if (min(i, j) <= 1u) return i * j; u16 q = 8, eq = 1u << 8; u16 iu = i >> q, il = i & (eq - 1); u16 ju = j >> q, jl = j & (eq - 1); u16 u = c8.dp[iu][ju]; u16 l = c8.dp[il][jl]; u16 ul = c8.dp[iu ^ il][ju ^ jl]; u16 uq = c8.dp[u][eq >> 1]; return ((ul ^ l) << q) ^ uq ^ l; } public: constexpr calc16() : base(), exp(), log() { base[0] = 1; for (int i = 1; i < 16; i++) base[i] = naive(base[i - 1], proot); exp[0] = 1; for (int i = 1; i < order; i++) exp[i] = d(exp[i - 1]); u16* pre = exp + order + 1; pre[0] = 0; for (int b = 0; b < 16; b++) { int is = 1 << b, ie = is << 1; for (int i = is; i < ie; i++) pre[i] = pre[i - is] ^ base[b]; } for (int i = 0; i < order; i++) exp[i] = pre[exp[i]], log[exp[i]] = i; int ie = 2 * order + 30; for (int i = order; i < ie; i++) exp[i] = exp[i - order]; for (unsigned int i = ie; i < sizeof(exp) / sizeof(u16); i++) exp[i] = 0; log[0] = ie + 1; } constexpr u16 prod(u16 i, u16 j) const { return exp[log[i] + log[j]]; } // exp[3] = 2^{15} = 32768 constexpr u16 Hprod(u16 i, u16 j) const { return exp[log[i] + log[j] + 3]; } constexpr u16 H(u16 i) const { return exp[log[i] + 3]; } constexpr u16 H2(u16 i) const { return exp[log[i] + 6]; } } constexpr c16; constexpr u32 product32(u32 i, u32 j) { u16 iu = i >> 16, il = i & 65535; u16 ju = j >> 16, jl = j & 65535; u16 l = c16.prod(il, jl); u16 ul = c16.prod(iu ^ il, ju ^ jl); u16 uq = c16.Hprod(iu, ju); return (u32(ul ^ l) << 16) ^ uq ^ l; } // (+ : xor, x : nim product, * : integer product) // i x j // = (iu x ju + il x ju + iu x ji) * 2^{16} // + (iu x ju x 2^{15}) + il x jl // // assign ju = 2^{15}, jl = 0s // -> i x j // = ((iu + il) x 2^{15}) * 2^{16} + (iu x 2^{15} x 2^{15}) constexpr u32 H(u32 i) { u16 iu = i >> 16; u16 il = i & 65535; return (u32(c16.H(iu ^ il)) << 16) ^ c16.H2(iu); } constexpr u64 product64(u64 i, u64 j) { u32 iu = i >> 32, il = i & u32(-1); u32 ju = j >> 32, jl = j & u32(-1); u32 l = product32(il, jl); u32 ul = product32(iu ^ il, ju ^ jl); u32 uq = H(product32(iu, ju)); return (u64(ul ^ l) << 32) ^ uq ^ l; } } // namespace NimberImpl template struct NimberBase { using N = NimberBase; uint x; NimberBase() : x(0) {} NimberBase(uint _x) : x(_x) {} static N id0() { return {}; } static N id1() { return {1}; } N& operator+=(const N& p) { x ^= p.x; return *this; } N& operator-=(const N& p) { x ^= p.x; return *this; } N& operator*=(const N& p) { x = prod(x, p.x); return *this; } N operator+(const N& p) const { return x ^ p.x; } N operator-(const N& p) const { return x ^ p.x; } N operator*(const N& p) const { return prod(x, p.x); } bool operator==(const N& p) const { return x == p.x; } bool operator!=(const N& p) const { return x != p.x; } friend ostream& operator<<(ostream& os, const N& p) { return os << p.x; } }; using Nimber32 = NimberBase; using Nimber64 = NimberBase; /** * @brief Nim Product * @docs docs/math/nim-product.md */ 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; using namespace Nyaan; Nimber64 dp[2][2][128][128]; Nimber64 nx[2][2][128][128]; Nimber64 w[128][128]; void Nyaan::solve() { i64 N, M, X, Y, Z, u, v; cin >> N >> M >> X >> Y >> Z; --X, --Y, --Z; rep(i, N) rep(j, i) { u64 x = u64(rng()) % u64(-1) + 1; w[i][j] = w[j][i] = x; } rep(i, M) { cin >> u >> v; --u, --v; w[u][v] = w[v][u] = 0; } // 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) { memset(nx, 0, sizeof(nx)); rep(ky, 2) rep(kz, 2) rep(c, N) rep(d, N) { if (w[c][d] == 0) continue; if (ky == 1 and d == Y) continue; if (kz == 1 and d == Z) continue; int nky = ky | (d == Y), nkz = kz | (d == Z); rep(p, N) if (p != d) nx[nky][nkz][d][c] += dp[ky][kz][c][p]; } rep(ky, 2) rep(kz, 2) rep(i, N) rep(j, N) { if (w[i][j] != 0) nx[ky][kz][i][j] *= w[i][j]; } swap(dp, nx); rep(i, N) if (dp[1][1][X][i] != 0) die(L); } die(-1); }