#ifdef LOCAL class SS { int x[0]; }; extern "C" SS __sanitizer_print_stack_trace(); #define __last_state \ } \ ; \ SS x { \ __sanitizer_print_stack_trace() #endif #include <bits/stdc++.h> #include <chrono> #include <ext/pb_ds/assoc_container.hpp> #include <math.h> using namespace __gnu_pbds; using namespace std; #define endl "\n" #define mp make_pair #define st first #define nd second #define pii pair<int, int> #define vi vector<int> #define pb push_back #define _upgrade ios_base::sync_with_stdio(0), cout.setf(ios::fixed), cout.precision(10), cin.tie(0), cout.tie(0); #define rep(i, n) for (int i = 0; i < (n); ++i) #define fwd(i, a, b) for (int i = (a); i < (b); ++i) #define trav(a, x) for (auto &a : x) #define all(c) (c).begin(), (c).end() #define sz(X) (int)((X).size()) typedef long double ld; typedef unsigned long long ull; typedef long long ll; typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> indexed_set; // find_by_order(x) <-returns x-th element order_of_key(x) <- returns order of element x // mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());uniform_int_distribution<int> distr(0, 1e9);auto my_rand = bind(distr, gen); // my_rand() zwraca teraz liczbe z przedzialu [a, b] #ifdef LOCAL ostream &operator<<(ostream &out, string str) { for (char c : str) out << c; return out; } template <class L, class R> ostream &operator<<(ostream &out, pair<L, R> p) { return out << "(" << p.st << ", " << p.nd << ")"; } template <class L, class R, class S> ostream &operator<<(ostream &out, tuple<L, R, S> p) { auto &[a, b, c] = p; return out << "(" << a << ", " << b << ", " << c << ")"; } template <class T> auto operator<<(ostream &out, T a) -> decltype(a.begin(), out) { out << '{'; for (auto it = a.begin(); it != a.end(); it = next(it)) out << (it != a.begin() ? ", " : "") << *it; return out << '}'; } void dump() { cerr << "\n"; } template <class T, class... Ts> void dump(T a, Ts... x) { cerr << a << ", "; dump(x...); } #define debug(...) cerr << "[" #__VA_ARGS__ "]: ", dump(__VA_ARGS__) #else #define debug(...) ; #endif #define int long long const ll mod = 1e9 + 7; ull mod_mul(ull a, ull b) { return a * b % mod; } ull mod_pow(ull b, ull e) { ull ans = 1; for (; e; b = b * b % mod, e /= 2) if (e & 1) ans = ans * b % mod; return ans; } ull inv(ull a) { return mod_pow(a, mod - 2); } const int MAXF = 2e5 + 99; const int MAXN = MAXF; ll F[MAXF], I[MAXF]; void pre() { F[0] = I[0] = 1; for (int i = 1; i < MAXF; i++) { F[i] = mod_mul(i, F[i - 1]); I[i] = inv(F[i]); } } ll binom(int a, int b) { assert(a >= b); return mod_mul(mod_mul(F[a], I[b]), I[a - b]); } int pt2(int x) { int res = 0; rep(i, x + 1) res += binom(x, i); return res % mod; } #define DWA 2 int clr[MAXN]; vector<int> G[MAXN]; vector<int> T; void dfs(int x, bool &good) { T.push_back(x); for (int y : G[x]) { if (!clr[y]) { clr[y] = clr[x] ^ 1; dfs(y, good); } good = good and (clr[y] == (clr[x] ^ 1)); } } int32_t main() { _upgrade; pre(); int n, m; cin >> n >> m; vector<int> S(n); for (auto &s : S) cin >> s; rep(i, m) { int a, b; cin >> a >> b; G[--a].push_back(--b); G[b].push_back(a); } int res = 1; rep(i, n) if (!clr[i]) { clr[i] = DWA; bool dwudzielny = true; T.clear(); dfs(i, dwudzielny); debug(T, dwudzielny); if (!dwudzielny) res = res * pt2(sz(T) - 1) % mod; else { int ile[2] = {0, 0}; int ilec[2] = {0, 0}; for (int t : T) { int idx = (clr[t] == DWA); ile[idx]++; ilec[idx] += S[t]; } int _tmp = 0; for (int t = -min(ilec[0], ilec[1]); t <= min(ile[0] - ilec[0], ile[1] - ilec[1]); t++) { auto A = binom(ile[0], ilec[0] + t); auto B = binom(ile[1], ilec[1] + t); _tmp += A * B % mod; } res = res * (_tmp % mod) % mod; } } cout << res << endl; }
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 | #ifdef LOCAL class SS { int x[0]; }; extern "C" SS __sanitizer_print_stack_trace(); #define __last_state \ } \ ; \ SS x { \ __sanitizer_print_stack_trace() #endif #include <bits/stdc++.h> #include <chrono> #include <ext/pb_ds/assoc_container.hpp> #include <math.h> using namespace __gnu_pbds; using namespace std; #define endl "\n" #define mp make_pair #define st first #define nd second #define pii pair<int, int> #define vi vector<int> #define pb push_back #define _upgrade ios_base::sync_with_stdio(0), cout.setf(ios::fixed), cout.precision(10), cin.tie(0), cout.tie(0); #define rep(i, n) for (int i = 0; i < (n); ++i) #define fwd(i, a, b) for (int i = (a); i < (b); ++i) #define trav(a, x) for (auto &a : x) #define all(c) (c).begin(), (c).end() #define sz(X) (int)((X).size()) typedef long double ld; typedef unsigned long long ull; typedef long long ll; typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> indexed_set; // find_by_order(x) <-returns x-th element order_of_key(x) <- returns order of element x // mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());uniform_int_distribution<int> distr(0, 1e9);auto my_rand = bind(distr, gen); // my_rand() zwraca teraz liczbe z przedzialu [a, b] #ifdef LOCAL ostream &operator<<(ostream &out, string str) { for (char c : str) out << c; return out; } template <class L, class R> ostream &operator<<(ostream &out, pair<L, R> p) { return out << "(" << p.st << ", " << p.nd << ")"; } template <class L, class R, class S> ostream &operator<<(ostream &out, tuple<L, R, S> p) { auto &[a, b, c] = p; return out << "(" << a << ", " << b << ", " << c << ")"; } template <class T> auto operator<<(ostream &out, T a) -> decltype(a.begin(), out) { out << '{'; for (auto it = a.begin(); it != a.end(); it = next(it)) out << (it != a.begin() ? ", " : "") << *it; return out << '}'; } void dump() { cerr << "\n"; } template <class T, class... Ts> void dump(T a, Ts... x) { cerr << a << ", "; dump(x...); } #define debug(...) cerr << "[" #__VA_ARGS__ "]: ", dump(__VA_ARGS__) #else #define debug(...) ; #endif #define int long long const ll mod = 1e9 + 7; ull mod_mul(ull a, ull b) { return a * b % mod; } ull mod_pow(ull b, ull e) { ull ans = 1; for (; e; b = b * b % mod, e /= 2) if (e & 1) ans = ans * b % mod; return ans; } ull inv(ull a) { return mod_pow(a, mod - 2); } const int MAXF = 2e5 + 99; const int MAXN = MAXF; ll F[MAXF], I[MAXF]; void pre() { F[0] = I[0] = 1; for (int i = 1; i < MAXF; i++) { F[i] = mod_mul(i, F[i - 1]); I[i] = inv(F[i]); } } ll binom(int a, int b) { assert(a >= b); return mod_mul(mod_mul(F[a], I[b]), I[a - b]); } int pt2(int x) { int res = 0; rep(i, x + 1) res += binom(x, i); return res % mod; } #define DWA 2 int clr[MAXN]; vector<int> G[MAXN]; vector<int> T; void dfs(int x, bool &good) { T.push_back(x); for (int y : G[x]) { if (!clr[y]) { clr[y] = clr[x] ^ 1; dfs(y, good); } good = good and (clr[y] == (clr[x] ^ 1)); } } int32_t main() { _upgrade; pre(); int n, m; cin >> n >> m; vector<int> S(n); for (auto &s : S) cin >> s; rep(i, m) { int a, b; cin >> a >> b; G[--a].push_back(--b); G[b].push_back(a); } int res = 1; rep(i, n) if (!clr[i]) { clr[i] = DWA; bool dwudzielny = true; T.clear(); dfs(i, dwudzielny); debug(T, dwudzielny); if (!dwudzielny) res = res * pt2(sz(T) - 1) % mod; else { int ile[2] = {0, 0}; int ilec[2] = {0, 0}; for (int t : T) { int idx = (clr[t] == DWA); ile[idx]++; ilec[idx] += S[t]; } int _tmp = 0; for (int t = -min(ilec[0], ilec[1]); t <= min(ile[0] - ilec[0], ile[1] - ilec[1]); t++) { auto A = binom(ile[0], ilec[0] + t); auto B = binom(ile[1], ilec[1] + t); _tmp += A * B % mod; } res = res * (_tmp % mod) % mod; } } cout << res << endl; } |