CSES Giant Pizza
// 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);
#else
#define debug(x...)
#define Debug(x...)
#endif
template<typename...Args> void print_(Args...args){((cout<<args<<" "),...)<<endl;}
#define VI vector<int>
#define VII vector<vector<int>>
#define VIII vector<vector<vector<int>>>
#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 double long double
#define int long long
#define MAXN 200010

struct graph {
    struct node {
        int v, w;
        bool operator<(const node &other) const {
            return w < other.w;
        }
        bool operator==(const node &other) const {
            return v == other.v && w == other.w;
        }
    };
    vector<vector<node>> e;
    int n;
    bool directed;
    graph(int V, bool D = 0) {
        n = V;
        e.resize(n);
        directed = D;
    }
    void add_edge(int u, int v, int w = 1) {
        e[u].push_back(node{v, w});
    }
    void tarjan_scc(vector<vector<int>> &scc, vector<int> &belong) {
        stack<int> s;
        vector<int> dfn(n), low(n), instack(n);
        int dfncnt;
        scc.clear(), belong.resize(n, -1);
        function<void(int)> dfs = [&](int u) {
            low[u] = dfn[u] = ++dfncnt, s.push(u), instack[u] = 1;
            for (auto edge: e[u]) {
                int v = edge.v;
                if (!dfn[v]) dfs(v), cmin(low[u], low[v]);
                else if (instack[v]) cmin(low[u], dfn[v]);
            }
            if (dfn[u] == low[u]) {
                scc.push_back(vector<int>{});
                while (s.top() != u) {
                    belong[s.top()] = sz(scc) - 1;
                    scc.back().push_back(s.top());
                    instack[s.top()] = 0, s.pop();
                }
                belong[s.top()] = sz(scc) - 1;
                scc.back().push_back(s.top());
                instack[s.top()] = 0, s.pop();
            }
        };
        rep(i, 0, n) if (!~belong[i]) dfs(i);
    }
    int topo(vector<int> &vs) {
        vector<int> din(n, 0);
        for (auto es: e) for (auto edge: es) ++din[edge.v];
        queue<int> q;
        rep(i, 0, n) if (!din[i]) q.push(i);
        vs.clear();
        while (!q.empty()) {
            int u = q.front(); q.pop();
            vs.push_back(u);
            for (auto [v, _]: e[u]) {
                if (!--din[v]) q.push(v);
            }
        }
        return sz(vs) == n;
    }
    graph contract(vector<vector<int>> &scc, vector<int> &belong) {
        tarjan_scc(scc, belong);
        int V = sz(scc);
        graph dag(V, 1);
        vector<int> vis(V, 0);
        for (auto comp: scc) {
            for (auto u: comp) {
                for (auto edge: e[u]) {
                    int v = edge.v;
                    if (belong[u] != belong[v]) {
                        dag.add_edge(belong[u], belong[v]);
                        vis[belong[v]] = 1;
                    }
                }
            }
            for (auto u: comp) for (auto edge: e[u]) if (belong[u] != belong[edge.v]) vis[belong[edge.v]] = 0;
        }
        return dag;
    }
    int twosat(vector<int> &ans) {
        vector<vector<int>> scc; vector<int> belong; auto dag = contract(scc, belong);
        int V = n >> 1;
        rep(i, 0, V) if (belong[i] == belong[i + V]) return 0;
        vector<int> vs; dag.topo(vs);
        vector<int> idx(dag.n);
        rep(i, 0, dag.n) idx[vs[i]] = i;
        ans.assign(V, 0);
        rep(i, 0, V) if (idx[belong[i]] > idx[belong[i + V]]) ans[i] = 1;
        return 1;
    }
    void graphviz_dump(string filename = "graph.dot") {
        ofstream gf; gf.open(filename);
        gf << (directed ? "digraph" : "graph") << " {\n";
        gf << "    "; rep(i, 0, n) gf << i << " ;"[i==n-1]; gf << endl;
        string notation = directed ? " -> " : " -- ";
        bool weighted = 0;
        for (auto es: e) for (auto edge: es) if (edge.w != 1) weighted = 1;
        rep(u, 0, n) {
            for (auto [v, w]: e[u]) {
                if (!directed && u > v) continue;
                gf << "    " << u << notation << v << (weighted ? " ;\n" : ";\n");
            }
        }
        gf << "}\n";
    }
};

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

    int n, m; cin >> n >> m;
    graph g(2*m, 1);
    rep(i, 0, n) {
        string su, sv; int u, v; cin >> su >> u >> sv >> v; --u, --v;
        if (su[0] == '+' && sv[0] == '+') g.add_edge(m+u, v), g.add_edge(m+v, u);
        else if (su[0] == '-' && sv[0] == '-') g.add_edge(u, m+v), g.add_edge(v, m+u);
        else if (su[0] == '+' && sv[0] == '-') g.add_edge(m+u, m+v), g.add_edge(v, u);
        else if (su[0] == '-' && sv[0] == '+') g.add_edge(u, v), g.add_edge(m+v, m+u);
    }
    // g.graphviz_dump();
    vector<int> ans;
    int valid = g.twosat(ans);
    if (!valid) cout << "IMPOSSIBLE" << endl;
    else {
        rep(i, 0, m) cout << (ans[i] ? '+' : '-') << " ";
        cout << endl;
    }

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