#include <algorithm> #include <bitset> #include <complex> #include <deque> #include <exception> #include <fstream> #include <functional> #include <iomanip> #include <ios> #include <iosfwd> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <locale> #include <map> #include <memory> #include <new> #include <numeric> #include <ostream> #include <queue> #include <set> #include <sstream> #include <stack> #include <stdexcept> #include <streambuf> #include <string> #include <typeinfo> #include <utility> #include <valarray> #include <vector> #include <stdio.h> #include <string.h> #include <array> #include <atomic> #include <chrono> #include <condition_variable> #include <forward_list> #include <future> #include <initializer_list> #include <mutex> #include <random> #include <ratio> #include <regex> #include <scoped_allocator> #include <system_error> #include <thread> #include <tuple> #include <typeindex> #include <type_traits> #include <unordered_map> #include <unordered_set> #include <cassert> using namespace std; void __print(int x) {cerr << x;} void __print(long x) {cerr << x;} void __print(long long x) {cerr << x;} void __print(unsigned x) {cerr << x;} void __print(unsigned long x) {cerr << x;} void __print(unsigned long long x) {cerr << x;} void __print(float x) {cerr << x;} void __print(double x) {cerr << x;} void __print(long double x) {cerr << x;} void __print(char x) {cerr << '\'' << x << '\'';} void __print(const char *x) {cerr << '\"' << x << '\"';} void __print(const string &x) {cerr << '\"' << x << '\"';} void __print(bool x) {cerr << (x ? "true" : "false");} template<typename T, typename V> void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';} template<typename T> void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";} void _print() {cerr << "]\n";} template <typename T, typename... V> void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);} #ifndef ONLINE_JUDGE #define debug(x...) cerr << "[" << #x << "] = ["; _print(x) #else #define debug(x...) #endif #define int long long #define all(x) x.begin(), x.end() #define pb push_back #define ll long long #define ii pair<int,int> #define vi vector<int> #define vll vector<ll> #define vii vector<ii> #define vvi vector<vi> #define fi first #define se second #define ld long double const int MOD = 1000000007; const int MAXN = 200005; vi fac(MAXN, 1), fac_inv(MAXN, 1); int bin_pow(int x, int n) { if(n == 0) return 1; if(n % 2) return (x * bin_pow(x, n-1)) % MOD; int half = bin_pow(x, n/2); return (half * half) % MOD; } void precalc() { for(int i = 1; i < MAXN; i++) { fac[i] = (fac[i-1] * i) % MOD; fac_inv[i] = bin_pow(fac[i], MOD - 2); } } int binom(int n, int k) { return ((fac[n] * fac_inv[k]) % MOD * fac_inv[n - k]) % MOD; } void test_case() { int n, m; cin >> n >> m; vi vec(n + 1); for(int i = 1; i <= n; i++) cin >> vec[i]; vvi adj(n + 1); for(int i = 1; i <= m; i++) { int u, v; cin >> u >> v; adj[u].pb(v); adj[v].pb(u); } vi dist(n + 1, -1); vi vis(n + 1, 0); auto fun = [&](int u) { queue<int> q; vi cnt(2, 0), sajz(2, 0); bool f = false; q.push(u); vis[u] = 1; dist[u] = 0; while(q.size() > 0) { int cur = q.front(); q.pop(); vis[cur] = 1; cnt[dist[cur]] += vec[cur]; sajz[dist[cur]]++; for(auto v : adj[cur]) { if(dist[v] == -1) { dist[v] = 1 ^ dist[cur]; q.push(v); } if(dist[v] == dist[cur]) { f = 1; } } } return vi{f, sajz[0], sajz[1], cnt[0], cnt[1]}; }; int ans = 1; for(int i = 1; i <= n; i++) { if(!vis[i]) { auto res = fun(i); int f = res[0], s1 = res[1], s2 = res[2], c1 = res[3], c2 = res[4]; if(f) { int st = (c1 + c2) % 2, to_add = 0; for(int j = st; j <= s1 + s2; j += 2) { to_add += binom(s1 + s2, j); to_add %= MOD; } ans *= to_add; ans %= MOD; } else { int mini = min(c1, c2), to_add = 0; c1 -= mini, c2 -= mini; for( ; c1 <= s1 && c2 <= s2; c1++, c2++) { to_add += (binom(s1, c1) * binom(s2, c2)) % MOD; to_add %= MOD; } ans *= to_add; ans %= MOD; } } } cout << ans << "\n"; } int32_t main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); precalc(); int tc = 1; // cin >> tc; while(tc--) { test_case(); } 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 | #include <algorithm> #include <bitset> #include <complex> #include <deque> #include <exception> #include <fstream> #include <functional> #include <iomanip> #include <ios> #include <iosfwd> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <locale> #include <map> #include <memory> #include <new> #include <numeric> #include <ostream> #include <queue> #include <set> #include <sstream> #include <stack> #include <stdexcept> #include <streambuf> #include <string> #include <typeinfo> #include <utility> #include <valarray> #include <vector> #include <stdio.h> #include <string.h> #include <array> #include <atomic> #include <chrono> #include <condition_variable> #include <forward_list> #include <future> #include <initializer_list> #include <mutex> #include <random> #include <ratio> #include <regex> #include <scoped_allocator> #include <system_error> #include <thread> #include <tuple> #include <typeindex> #include <type_traits> #include <unordered_map> #include <unordered_set> #include <cassert> using namespace std; void __print(int x) {cerr << x;} void __print(long x) {cerr << x;} void __print(long long x) {cerr << x;} void __print(unsigned x) {cerr << x;} void __print(unsigned long x) {cerr << x;} void __print(unsigned long long x) {cerr << x;} void __print(float x) {cerr << x;} void __print(double x) {cerr << x;} void __print(long double x) {cerr << x;} void __print(char x) {cerr << '\'' << x << '\'';} void __print(const char *x) {cerr << '\"' << x << '\"';} void __print(const string &x) {cerr << '\"' << x << '\"';} void __print(bool x) {cerr << (x ? "true" : "false");} template<typename T, typename V> void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';} template<typename T> void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";} void _print() {cerr << "]\n";} template <typename T, typename... V> void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);} #ifndef ONLINE_JUDGE #define debug(x...) cerr << "[" << #x << "] = ["; _print(x) #else #define debug(x...) #endif #define int long long #define all(x) x.begin(), x.end() #define pb push_back #define ll long long #define ii pair<int,int> #define vi vector<int> #define vll vector<ll> #define vii vector<ii> #define vvi vector<vi> #define fi first #define se second #define ld long double const int MOD = 1000000007; const int MAXN = 200005; vi fac(MAXN, 1), fac_inv(MAXN, 1); int bin_pow(int x, int n) { if(n == 0) return 1; if(n % 2) return (x * bin_pow(x, n-1)) % MOD; int half = bin_pow(x, n/2); return (half * half) % MOD; } void precalc() { for(int i = 1; i < MAXN; i++) { fac[i] = (fac[i-1] * i) % MOD; fac_inv[i] = bin_pow(fac[i], MOD - 2); } } int binom(int n, int k) { return ((fac[n] * fac_inv[k]) % MOD * fac_inv[n - k]) % MOD; } void test_case() { int n, m; cin >> n >> m; vi vec(n + 1); for(int i = 1; i <= n; i++) cin >> vec[i]; vvi adj(n + 1); for(int i = 1; i <= m; i++) { int u, v; cin >> u >> v; adj[u].pb(v); adj[v].pb(u); } vi dist(n + 1, -1); vi vis(n + 1, 0); auto fun = [&](int u) { queue<int> q; vi cnt(2, 0), sajz(2, 0); bool f = false; q.push(u); vis[u] = 1; dist[u] = 0; while(q.size() > 0) { int cur = q.front(); q.pop(); vis[cur] = 1; cnt[dist[cur]] += vec[cur]; sajz[dist[cur]]++; for(auto v : adj[cur]) { if(dist[v] == -1) { dist[v] = 1 ^ dist[cur]; q.push(v); } if(dist[v] == dist[cur]) { f = 1; } } } return vi{f, sajz[0], sajz[1], cnt[0], cnt[1]}; }; int ans = 1; for(int i = 1; i <= n; i++) { if(!vis[i]) { auto res = fun(i); int f = res[0], s1 = res[1], s2 = res[2], c1 = res[3], c2 = res[4]; if(f) { int st = (c1 + c2) % 2, to_add = 0; for(int j = st; j <= s1 + s2; j += 2) { to_add += binom(s1 + s2, j); to_add %= MOD; } ans *= to_add; ans %= MOD; } else { int mini = min(c1, c2), to_add = 0; c1 -= mini, c2 -= mini; for( ; c1 <= s1 && c2 <= s2; c1++, c2++) { to_add += (binom(s1, c1) * binom(s2, c2)) % MOD; to_add %= MOD; } ans *= to_add; ans %= MOD; } } } cout << ans << "\n"; } int32_t main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); precalc(); int tc = 1; // cin >> tc; while(tc--) { test_case(); } return 0; } |