// clang-format off #pragma GCC optimize("O3,unroll-loops") // #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt") #include <bits/stdc++.h> // #include <ext/pb_ds/assoc_container.hpp> // #include <ext/pb_ds/tree_policy.hpp> using namespace std; template<class Fun> class y_combinator_result { Fun fun_; public: template<class T> explicit y_combinator_result(T &&fun): fun_(forward<T>(fun)) {} template<class ...Args> decltype(auto) operator()(Args &&...args) { return fun_(ref(*this), forward<Args>(args)...); } }; template<class Fun> decltype(auto) y_combinator(Fun &&fun) { return y_combinator_result<decay_t<Fun>>(forward<Fun>(fun)); } // using namespace __gnu_pbds; // template <typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; #define sim template < class c #define ris return * this #define dor > debug & operator << #define eni(x) sim > typename enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) { sim > struct rge { c b, e; }; sim > rge<c> range(c i, c j) { return rge<c>{i, j}; } sim > auto dud(c* x) -> decltype(cerr << *x, 0); sim > char dud(...); struct debug { #ifdef XOX ~debug() { cerr << endl; } eni(!=) cerr << boolalpha << i; ris; } eni(==) ris << range(begin(i), end(i)); } sim, class b dor(pair < b, c > d) { ris << "(" << d.first << ", " << d.second << ")"; } sim dor(rge<c> d) { *this << "["; for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it; ris << "]"; } #else sim dor(const c&) { ris; } #endif }; #define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] " struct { template <class T> operator T() { T x; cin >> x; return x; } } in; #define endl '\n' #define pb emplace_back #define all(x) begin(x), end(x) #define sz(x) (int)(x).size() using i64 = long long; template <class T> using vt = vector<T>; template <class T, size_t n> using ar = array<T, n>; namespace R = ranges; auto ra(auto x, auto y) { return R::iota_view(x, y); } auto rae(auto x, auto y) { return ra(x, y + 1); } // #define int long long template <class T> T power(T a, i64 b) { T res = 1; for (; b; b /= 2, a *= a) if (b % 2) res *= a; return res; } template <int P> struct MInt { int x; MInt() : x{} {} MInt(i64 _x) : x{norm(_x % P)} {} int norm(int _x) const { if (_x < 0) _x += P; if (_x >= P) _x -= P; return _x; } int val() const { return x; } explicit operator int() const { return x; } MInt operator-() const { MInt res; res.x = norm(P - x); return res; } MInt inv() const { assert(x != 0); return power(*this, P - 2); } MInt &operator*=(MInt rhs) { x = (i64)x * rhs.x % P; return *this; } MInt &operator+=(MInt rhs) { x = norm(x + rhs.x); return *this; } MInt &operator-=(MInt rhs) { x = norm(x - rhs.x); return *this; } MInt &operator/=(MInt rhs) { return *this *= rhs.inv(); } friend MInt operator*(MInt lhs, MInt rhs) { MInt res = lhs; res *= rhs; return res; } friend MInt operator+(MInt lhs, MInt rhs) { MInt res = lhs; res += rhs; return res; } friend MInt operator-(MInt lhs, MInt rhs) { MInt res = lhs; res -= rhs; return res; } friend MInt operator/(MInt lhs, MInt rhs) { MInt res = lhs; res /= rhs; return res; } friend istream &operator>>(istream &is, MInt &a) { i64 v; is >> v; a = MInt(v); return is; } friend ostream &operator<<(ostream &os, const MInt &a) { return os << a.val(); } friend bool operator==(MInt lhs, MInt rhs) { return lhs.val() == rhs.val(); } friend bool operator!=(MInt lhs, MInt rhs) { return lhs.val() != rhs.val(); } }; const int P = 1000 * 1000 * 1000 + 7; using Z = MInt<P>; struct Comb { int n; vector<Z> _fac; vector<Z> _invfac; vector<Z> _inv; Comb() : n{0}, _fac{1}, _invfac{1}, _inv{0} {} Comb(int _n) : Comb() { init(_n); } void init(int m) { if (m <= n) return; _fac.resize(m + 1); _invfac.resize(m + 1); _inv.resize(m + 1); for (int i = n + 1; i <= m; i++) _fac[i] = _fac[i - 1] * i; _invfac[m] = _fac[m].inv(); for (int i = m; i > n; i--) { _invfac[i - 1] = _invfac[i] * i; _inv[i] = _invfac[i] * _fac[i - 1]; } n = m; } Z fac(int m) { if (m > n) init(2 * m); return _fac[m]; } Z invfac(int m) { if (m > n) init(2 * m); return _invfac[m]; } Z binom(int _n, int m) { if (_n < m || m < 0) return 0; return fac(_n) * invfac(m) * invfac(_n - m); } } comb; // clang-format on void solve() { int n = in, m = in; vt<bool> v; for (int i : ra(0, n)) { int x = in; v.pb(x); } vt<vt<int>> g(n); for (int i : ra(0, m)) { int a = in, b = in; --a, --b; g[a].pb(b); g[b].pb(a); } vt<int> col(n, -1); vt<int> spo; auto work = [&](int u) -> bool { queue<int> q; q.push(u); col[u] = 0; bool ok = true; spo.clear(); while (!q.empty()) { int u = q.front(); q.pop(); spo.pb(u); for (int to : g[u]) { if (col[to] == -1) { col[to] = col[u] ^ 1; q.push(to); } else { ok &= col[to] != col[u]; } } } return ok; }; Comb comb; Z ans = 1; for (int i : ra(0, n)) { if (col[i] == -1) { if (!work(i)) { ans *= power(Z(2), sz(spo) - 1); } else { if (sz(spo) == 1) continue; int kurdebele = 0; ar<int, 2> c{0, 0}; for (int j : spo) { if (v[j] == 1) kurdebele += (col[j] ? +1 : -1); c[col[j]]++; } Z sum = 0; for (int l = 0; l <= c[1]; l++) { int r = l - kurdebele; if (r >= 0 && r <= c[0]) sum += comb.binom(c[1], l) * comb.binom(c[0], r); } ans *= sum; } } } cout << ans << endl; } int32_t main() { cin.tie(0)->sync_with_stdio(0); int t = 1; // int t = in; while (t--) { solve(); } }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 | // clang-format off #pragma GCC optimize("O3,unroll-loops") // #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt") #include <bits/stdc++.h> // #include <ext/pb_ds/assoc_container.hpp> // #include <ext/pb_ds/tree_policy.hpp> using namespace std; template<class Fun> class y_combinator_result { Fun fun_; public: template<class T> explicit y_combinator_result(T &&fun): fun_(forward<T>(fun)) {} template<class ...Args> decltype(auto) operator()(Args &&...args) { return fun_(ref(*this), forward<Args>(args)...); } }; template<class Fun> decltype(auto) y_combinator(Fun &&fun) { return y_combinator_result<decay_t<Fun>>(forward<Fun>(fun)); } // using namespace __gnu_pbds; // template <typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; #define sim template < class c #define ris return * this #define dor > debug & operator << #define eni(x) sim > typename enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) { sim > struct rge { c b, e; }; sim > rge<c> range(c i, c j) { return rge<c>{i, j}; } sim > auto dud(c* x) -> decltype(cerr << *x, 0); sim > char dud(...); struct debug { #ifdef XOX ~debug() { cerr << endl; } eni(!=) cerr << boolalpha << i; ris; } eni(==) ris << range(begin(i), end(i)); } sim, class b dor(pair < b, c > d) { ris << "(" << d.first << ", " << d.second << ")"; } sim dor(rge<c> d) { *this << "["; for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it; ris << "]"; } #else sim dor(const c&) { ris; } #endif }; #define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] " struct { template <class T> operator T() { T x; cin >> x; return x; } } in; #define endl '\n' #define pb emplace_back #define all(x) begin(x), end(x) #define sz(x) (int)(x).size() using i64 = long long; template <class T> using vt = vector<T>; template <class T, size_t n> using ar = array<T, n>; namespace R = ranges; auto ra(auto x, auto y) { return R::iota_view(x, y); } auto rae(auto x, auto y) { return ra(x, y + 1); } // #define int long long template <class T> T power(T a, i64 b) { T res = 1; for (; b; b /= 2, a *= a) if (b % 2) res *= a; return res; } template <int P> struct MInt { int x; MInt() : x{} {} MInt(i64 _x) : x{norm(_x % P)} {} int norm(int _x) const { if (_x < 0) _x += P; if (_x >= P) _x -= P; return _x; } int val() const { return x; } explicit operator int() const { return x; } MInt operator-() const { MInt res; res.x = norm(P - x); return res; } MInt inv() const { assert(x != 0); return power(*this, P - 2); } MInt &operator*=(MInt rhs) { x = (i64)x * rhs.x % P; return *this; } MInt &operator+=(MInt rhs) { x = norm(x + rhs.x); return *this; } MInt &operator-=(MInt rhs) { x = norm(x - rhs.x); return *this; } MInt &operator/=(MInt rhs) { return *this *= rhs.inv(); } friend MInt operator*(MInt lhs, MInt rhs) { MInt res = lhs; res *= rhs; return res; } friend MInt operator+(MInt lhs, MInt rhs) { MInt res = lhs; res += rhs; return res; } friend MInt operator-(MInt lhs, MInt rhs) { MInt res = lhs; res -= rhs; return res; } friend MInt operator/(MInt lhs, MInt rhs) { MInt res = lhs; res /= rhs; return res; } friend istream &operator>>(istream &is, MInt &a) { i64 v; is >> v; a = MInt(v); return is; } friend ostream &operator<<(ostream &os, const MInt &a) { return os << a.val(); } friend bool operator==(MInt lhs, MInt rhs) { return lhs.val() == rhs.val(); } friend bool operator!=(MInt lhs, MInt rhs) { return lhs.val() != rhs.val(); } }; const int P = 1000 * 1000 * 1000 + 7; using Z = MInt<P>; struct Comb { int n; vector<Z> _fac; vector<Z> _invfac; vector<Z> _inv; Comb() : n{0}, _fac{1}, _invfac{1}, _inv{0} {} Comb(int _n) : Comb() { init(_n); } void init(int m) { if (m <= n) return; _fac.resize(m + 1); _invfac.resize(m + 1); _inv.resize(m + 1); for (int i = n + 1; i <= m; i++) _fac[i] = _fac[i - 1] * i; _invfac[m] = _fac[m].inv(); for (int i = m; i > n; i--) { _invfac[i - 1] = _invfac[i] * i; _inv[i] = _invfac[i] * _fac[i - 1]; } n = m; } Z fac(int m) { if (m > n) init(2 * m); return _fac[m]; } Z invfac(int m) { if (m > n) init(2 * m); return _invfac[m]; } Z binom(int _n, int m) { if (_n < m || m < 0) return 0; return fac(_n) * invfac(m) * invfac(_n - m); } } comb; // clang-format on void solve() { int n = in, m = in; vt<bool> v; for (int i : ra(0, n)) { int x = in; v.pb(x); } vt<vt<int>> g(n); for (int i : ra(0, m)) { int a = in, b = in; --a, --b; g[a].pb(b); g[b].pb(a); } vt<int> col(n, -1); vt<int> spo; auto work = [&](int u) -> bool { queue<int> q; q.push(u); col[u] = 0; bool ok = true; spo.clear(); while (!q.empty()) { int u = q.front(); q.pop(); spo.pb(u); for (int to : g[u]) { if (col[to] == -1) { col[to] = col[u] ^ 1; q.push(to); } else { ok &= col[to] != col[u]; } } } return ok; }; Comb comb; Z ans = 1; for (int i : ra(0, n)) { if (col[i] == -1) { if (!work(i)) { ans *= power(Z(2), sz(spo) - 1); } else { if (sz(spo) == 1) continue; int kurdebele = 0; ar<int, 2> c{0, 0}; for (int j : spo) { if (v[j] == 1) kurdebele += (col[j] ? +1 : -1); c[col[j]]++; } Z sum = 0; for (int l = 0; l <= c[1]; l++) { int r = l - kurdebele; if (r >= 0 && r <= c[0]) sum += comb.binom(c[1], l) * comb.binom(c[0], r); } ans *= sum; } } } cout << ans << endl; } int32_t main() { cin.tie(0)->sync_with_stdio(0); int t = 1; // int t = in; while (t--) { solve(); } } |