#include <algorithm> #include <array> #include <bitset> #include <cassert> #include <chrono> #include <cmath> #include <complex> #include <cstring> #include <functional> #include <iomanip> #include <iostream> #include <map> #include <numeric> #include <queue> #include <random> #include <set> #include <unordered_set> #include <vector> #include <climits> using namespace std; using ll = long long; using ul = unsigned long long; using db = long double; using pi = pair<int, int>; using vi = vector<int>; using vl = vector<ll>; using vpi = vector<pi>; #define mp make_pair #define pb push_back #define eb emplace_back #define x first #define y second template<class T> using V = vector<T>; template<class T, size_t SZ> using AR = array<T,SZ>; #define FOR(i,a,b) for (int i = (a); i < (b); ++i) #define F0R(i,a) FOR(i,0,a) #define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i) #define R0F(i,a) ROF(i,0,a) #define each(a,x) for (auto& a: x) #define sz(x) int((x).size()) #define all(x) (x).begin(), (x).end() #define rep(i,a,b) for(int i = (a); i < (b); i++) #define per(i,a,b) for(int i = (b) - 1; i >= (a); i--) #ifdef LOCAL template<class A, class B> auto& operator<<(auto &o, pair<A, B> p) { return o << '(' << p.x << ", " << p.y << ')'; } auto& operator<<(auto& o, auto a) { o << "{"; for (auto b : a) o << b << ", "; return o << "}"; } void dump(auto... x) { ((cerr << x << ", "), ...) << "\n"; } #define debug(x...) cerr << "[" #x "]: ", dump(x) #else #define debug(...) ; #endif template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; } template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; } template<class T> int lwb(V<T>& a, const T& b) { return int(lb(all(a),b)-bg(a)); } template<class T> int upb(V<T>& a, const T& b) { return int(ub(all(a),b)-bg(a)); } template<class T> void remDup(vector<T>& v) { sort(all(v)); v.erase(unique(all(v)),end(v)); } template<int MOD, int RT> struct mint { static const int mod = MOD; static constexpr mint rt() { return RT; } int v; explicit operator int() const { return v; } mint():v(0) {} mint(ll _v) { v = int((-MOD < _v && _v < MOD) ? _v : _v % MOD); if (v < 0) v += MOD; } bool operator==(const mint& o) const { return v == o.v; } friend bool operator!=(const mint& a, const mint& b) { return !(a == b); } friend bool operator<(const mint& a, const mint& b) { return a.v < b.v; } friend ostream& operator<<(ostream& os, mint& a) { return os << a.v; } friend istream& operator>>(istream& os, mint& a) { ll x; os >> x; a = mint(x); return os; } mint& operator+=(const mint& o) { if ((v += o.v) >= MOD) v -= MOD; return *this; } mint& operator-=(const mint& o) { if ((v -= o.v) < 0) v += MOD; return *this; } mint& operator*=(const mint& o) { v = int((ll)v*o.v%MOD); return *this; } mint& operator/=(const mint& o) { return (*this) *= inv(o); } friend mint pow(mint a, ll p) { mint ans = 1; assert(p >= 0); for (; p; p /= 2, a *= a) if (p&1) ans *= a; return ans; } friend mint inv(const mint& a) { assert(a.v != 0); return pow(a,MOD-2); } mint operator-() const { return mint(-v); } mint& operator++() { return *this += 1; } mint& operator--() { return *this -= 1; } friend mint operator+(mint a, const mint& b) { return a += b; } friend mint operator-(mint a, const mint& b) { return a -= b; } friend mint operator*(mint a, const mint& b) { return a *= b; } friend mint operator/(mint a, const mint& b) { return a /= b; } }; constexpr int MOD = 1e9+7; using mi = mint<MOD,5>; using vmi = V<mi>; const int N = 2e5+10; vi g[N]; int color[N]; bool vis[N]; bool flip[N]; void dfs_color(int u, int c) { vis[u] = true; color[u] = c; for (int v : g[u]) { if (vis[v]) continue; dfs_color(v, c ^ 1); } } int cur_component_size; void dfs_clear(int u) { vis[u] = true; cur_component_size++; for (int v : g[u]) { if (vis[v]) continue; dfs_clear(v); } } int n, m; mi res = 1; mi factorial[N]; mi inv_factorial[N]; void init() { factorial[0] = 1; rep(i,1,N) factorial[i] = factorial[i-1] * i; inv_factorial[N-1] = inv(factorial[N-1]); per(i,0,N-1) inv_factorial[i] = inv_factorial[i+1] * (i+1); } mi binom(int a, int b) { if (b > a || b < 0) return 0; return factorial[a] * inv_factorial[b] * inv_factorial[a - b]; } vi side[2]; void dfs_sides(int i) { vis[i] = true; side[color[i]].pb(i); for (int j : g[i]) { if (vis[j]) continue; dfs_sides(j); } } signed main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); init(); cin >> n >> m; rep(i,0,n) cin >> flip[i]; rep(i,0,m) { int a, b; cin >> a >> b; a--; b--; g[a].pb(b); g[b].pb(a); } rep(i,0,n) { if (!vis[i]) dfs_color(i, 0); } fill(vis, vis + n, false); rep(i,0,n) { if (vis[i]) continue; for (int v : g[i]) { if (color[v] == color[i]) { cur_component_size = 0; dfs_clear(i); res *= pow(mi(2), cur_component_size - 1); } } } rep(i,0,n) { if (vis[i]) continue; side[0].clear(); side[1].clear(); dfs_sides(i); int siz[2]; int zeros[2]; rep(j,0,2) { siz[j] = sz(side[j]); zeros[j] = 0; for (auto u : side[j]) { if (!flip[u]) zeros[j]++; } } if (zeros[0] == siz[0] && zeros[1] == 0) continue; if (zeros[1] == siz[1] && zeros[0] == 0) continue; mi cur = 0; rep(j,0,siz[0]+1) { cur += binom(siz[0], j) * binom(siz[1], zeros[1] - zeros[0] + j); } res *= cur; } cout << res << '\n'; return 0; }
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 | #include <algorithm> #include <array> #include <bitset> #include <cassert> #include <chrono> #include <cmath> #include <complex> #include <cstring> #include <functional> #include <iomanip> #include <iostream> #include <map> #include <numeric> #include <queue> #include <random> #include <set> #include <unordered_set> #include <vector> #include <climits> using namespace std; using ll = long long; using ul = unsigned long long; using db = long double; using pi = pair<int, int>; using vi = vector<int>; using vl = vector<ll>; using vpi = vector<pi>; #define mp make_pair #define pb push_back #define eb emplace_back #define x first #define y second template<class T> using V = vector<T>; template<class T, size_t SZ> using AR = array<T,SZ>; #define FOR(i,a,b) for (int i = (a); i < (b); ++i) #define F0R(i,a) FOR(i,0,a) #define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i) #define R0F(i,a) ROF(i,0,a) #define each(a,x) for (auto& a: x) #define sz(x) int((x).size()) #define all(x) (x).begin(), (x).end() #define rep(i,a,b) for(int i = (a); i < (b); i++) #define per(i,a,b) for(int i = (b) - 1; i >= (a); i--) #ifdef LOCAL template<class A, class B> auto& operator<<(auto &o, pair<A, B> p) { return o << '(' << p.x << ", " << p.y << ')'; } auto& operator<<(auto& o, auto a) { o << "{"; for (auto b : a) o << b << ", "; return o << "}"; } void dump(auto... x) { ((cerr << x << ", "), ...) << "\n"; } #define debug(x...) cerr << "[" #x "]: ", dump(x) #else #define debug(...) ; #endif template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; } template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; } template<class T> int lwb(V<T>& a, const T& b) { return int(lb(all(a),b)-bg(a)); } template<class T> int upb(V<T>& a, const T& b) { return int(ub(all(a),b)-bg(a)); } template<class T> void remDup(vector<T>& v) { sort(all(v)); v.erase(unique(all(v)),end(v)); } template<int MOD, int RT> struct mint { static const int mod = MOD; static constexpr mint rt() { return RT; } int v; explicit operator int() const { return v; } mint():v(0) {} mint(ll _v) { v = int((-MOD < _v && _v < MOD) ? _v : _v % MOD); if (v < 0) v += MOD; } bool operator==(const mint& o) const { return v == o.v; } friend bool operator!=(const mint& a, const mint& b) { return !(a == b); } friend bool operator<(const mint& a, const mint& b) { return a.v < b.v; } friend ostream& operator<<(ostream& os, mint& a) { return os << a.v; } friend istream& operator>>(istream& os, mint& a) { ll x; os >> x; a = mint(x); return os; } mint& operator+=(const mint& o) { if ((v += o.v) >= MOD) v -= MOD; return *this; } mint& operator-=(const mint& o) { if ((v -= o.v) < 0) v += MOD; return *this; } mint& operator*=(const mint& o) { v = int((ll)v*o.v%MOD); return *this; } mint& operator/=(const mint& o) { return (*this) *= inv(o); } friend mint pow(mint a, ll p) { mint ans = 1; assert(p >= 0); for (; p; p /= 2, a *= a) if (p&1) ans *= a; return ans; } friend mint inv(const mint& a) { assert(a.v != 0); return pow(a,MOD-2); } mint operator-() const { return mint(-v); } mint& operator++() { return *this += 1; } mint& operator--() { return *this -= 1; } friend mint operator+(mint a, const mint& b) { return a += b; } friend mint operator-(mint a, const mint& b) { return a -= b; } friend mint operator*(mint a, const mint& b) { return a *= b; } friend mint operator/(mint a, const mint& b) { return a /= b; } }; constexpr int MOD = 1e9+7; using mi = mint<MOD,5>; using vmi = V<mi>; const int N = 2e5+10; vi g[N]; int color[N]; bool vis[N]; bool flip[N]; void dfs_color(int u, int c) { vis[u] = true; color[u] = c; for (int v : g[u]) { if (vis[v]) continue; dfs_color(v, c ^ 1); } } int cur_component_size; void dfs_clear(int u) { vis[u] = true; cur_component_size++; for (int v : g[u]) { if (vis[v]) continue; dfs_clear(v); } } int n, m; mi res = 1; mi factorial[N]; mi inv_factorial[N]; void init() { factorial[0] = 1; rep(i,1,N) factorial[i] = factorial[i-1] * i; inv_factorial[N-1] = inv(factorial[N-1]); per(i,0,N-1) inv_factorial[i] = inv_factorial[i+1] * (i+1); } mi binom(int a, int b) { if (b > a || b < 0) return 0; return factorial[a] * inv_factorial[b] * inv_factorial[a - b]; } vi side[2]; void dfs_sides(int i) { vis[i] = true; side[color[i]].pb(i); for (int j : g[i]) { if (vis[j]) continue; dfs_sides(j); } } signed main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); init(); cin >> n >> m; rep(i,0,n) cin >> flip[i]; rep(i,0,m) { int a, b; cin >> a >> b; a--; b--; g[a].pb(b); g[b].pb(a); } rep(i,0,n) { if (!vis[i]) dfs_color(i, 0); } fill(vis, vis + n, false); rep(i,0,n) { if (vis[i]) continue; for (int v : g[i]) { if (color[v] == color[i]) { cur_component_size = 0; dfs_clear(i); res *= pow(mi(2), cur_component_size - 1); } } } rep(i,0,n) { if (vis[i]) continue; side[0].clear(); side[1].clear(); dfs_sides(i); int siz[2]; int zeros[2]; rep(j,0,2) { siz[j] = sz(side[j]); zeros[j] = 0; for (auto u : side[j]) { if (!flip[u]) zeros[j]++; } } if (zeros[0] == siz[0] && zeros[1] == 0) continue; if (zeros[1] == siz[1] && zeros[0] == 0) continue; mi cur = 0; rep(j,0,siz[0]+1) { cur += binom(siz[0], j) * binom(siz[1], zeros[1] - zeros[0] + j); } res *= cur; } cout << res << '\n'; return 0; } |