CSES Eulerian Subgraphs
// compile: make data
// run: ./data < data.in
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#ifdef LOCAL
#include <debug/codeforces.h>
#define debug(x...) _debug_print(#x, x);
#define Debug(x...) _debug_print_format(#x, x);
std::ifstream terminal("/dev/tty");
#define PP cerr<<"\033[1;30mpause...\e[0m",terminal.ignore();
#else
#define debug(x...)
#define Debug(x...)
#define PP
#endif
template<typename...Args> void print_(Args...args){((cout<<args<<" "),...)<<endl;}
#define rep(i,a,b) for(int i=(a);i<(int)(b);++i)
#define sz(v) ((int)(v).size())
#define print(...) print_(__VA_ARGS__);
#define FIND(a, x) ((find(a.begin(),a.end(),(x))!=a.end())?1:0)
#define cmin(x,...) x=min({(x),__VA_ARGS__})
#define cmax(x,...) x=max({(x),__VA_ARGS__})
#define INTMAX (int)(9223372036854775807)
#define INF (int)(1152921504606846976)
#define NaN (int)(0x8b88e1d0595d51d1)
#define double long double
#define int long long
#define uint unsigned long long
#define MAXN 200010
#define P 1000000007

int32_t main() {
    ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);

    int n, m; cin >> n >> m;
    vector<vector<int>> e(n);
    rep(i, 0, m) {
        int u, v; cin >> u >> v; --u, --v;
        e[u].push_back(v);
        e[v].push_back(u);
    }
    vector<int> vis(n, 0);
    function<void(int)> dfs = [&](int u) {
        vis[u] = 1;
        for (int v: e[u]) if (!vis[v]) dfs(v);
    };
    int cc = 0;
    rep(i, 0, n) if (!vis[i]) dfs(i), ++cc;
    function<int(int, int)> powmod = [&](int a, int b) {
        if (b == 0) return 1ll;
        if (b == 1) return a % P;
        int x = powmod(a, b / 2);
        return x * x % P * (b & 1 ? a : 1) % P;
    };
    cout << (powmod(2, m - n + cc)) << endl;

    return 0;
}
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Source: github.com/k4yt3x/flowerhd
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