Language: C++

#include <bits/stdc++.h>
#define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define pb push_back
using namespace std;
using ll = std::int_fast64_t;
using P = pair<ll, ll>;
constexpr ll inf = 1000000000;
constexpr ll mod = 998244353;
constexpr long double eps = 1e-15;
template<typename T1, typename T2>
ostream& operator<<(ostream& os, pair<T1, T2> p) {
    os << to_string(p.first) << " " << to_string(p.second);
    return os;
}
template<typename T>
ostream& operator<<(ostream& os, vector<T>& v) {
    REP(i, v.size()) {
        if(i) os << " ";
        os << to_string(v[i]);
    }
    return os;
}

struct modint {
    ll n;
public:
    modint(const ll n = 0) : n((n % mod + mod) % mod) {}
    static modint pow(modint a, int m) {
        modint r = 1;
        while(m > 0) {
            if(m & 1) { r *= a; }
            a = (a * a); m /= 2;
        }
        return r;
    }
    modint &operator++() { *this += 1; return *this; }
    modint &operator--() { *this -= 1; return *this; }
    modint operator++(int) { modint ret = *this; *this += 1; return ret; }
    modint operator--(int) { modint ret = *this; *this -= 1; return ret; }
    modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
    friend bool operator==(const modint& lhs, const modint& rhs) {
        return lhs.n == rhs.n;
    }
    friend bool operator<(const modint& lhs, const modint& rhs) {
        return lhs.n < rhs.n;
    }
    friend bool operator>(const modint& lhs, const modint& rhs) {
        return lhs.n > rhs.n;
    }
    friend modint &operator+=(modint& lhs, const modint& rhs) {
        lhs.n += rhs.n;
        if (lhs.n >= mod) lhs.n -= mod;
        return lhs;
    }
    friend modint &operator-=(modint& lhs, const modint& rhs) {
        lhs.n -= rhs.n;
        if (lhs.n < 0) lhs.n += mod;
        return lhs;
    }
    friend modint &operator*=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * rhs.n) % mod;
        return lhs;
    }
    friend modint &operator/=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * (~rhs).n) % mod;
        return lhs;
    }
    friend modint operator+(const modint& lhs, const modint& rhs) {
        return modint(lhs.n + rhs.n);
    }
    friend modint operator-(const modint& lhs, const modint& rhs) {
        return modint(lhs.n - rhs.n);
    }
    friend modint operator*(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * rhs.n);
    }
    friend modint operator/(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * (~rhs).n);
    }
};
istream& operator>>(istream& is, modint m) { is >> m.n; return is; }
ostream& operator<<(ostream& os, modint m) { os << m.n; return os; }

#define MAX_N 3030303
long long extgcd(long long a, long long b, long long& x, long long& y) {
    long long d = a;
    if (b != 0) {
        d = extgcd(b, a % b, y, x);
        y -= (a / b) * x;
    } else {
        x = 1; y = 0;
    }
    return d;
}
long long mod_inverse(long long a, long long m) {
    long long x, y;
    if(extgcd(a, m, x, y) == 1) return (m + x % m) % m;
    else return -1;
}
vector<long long> fact(MAX_N+1, inf);
long long mod_fact(long long n, long long& e) {
    if(fact[0] == inf) {
        fact[0]=1;
        if(MAX_N != 0) fact[1]=1;
        for(ll i = 2; i <= MAX_N; ++i) {
            fact[i] = (fact[i-1] * i) % mod;
        }
    }
    e = 0;
    if(n == 0) return 1;
    long long res = mod_fact(n / mod, e);
    e += n / mod;
    if((n / mod) % 2 != 0) return (res * (mod - fact[n % mod])) % mod;
    return (res * fact[n % mod]) % mod;
}
// return nCk
long long mod_comb(long long n, long long k) {
    if(n < 0 || k < 0 || n < k) return 0;
    long long e1, e2, e3;
    long long a1 = mod_fact(n, e1), a2 = mod_fact(k, e2), a3 = mod_fact(n - k, e3);
    if(e1 > e2 + e3) return 0;
    return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod;
}

class HopcroftKarp {
    vector< vector< int > > graph;
    vector< int > dist, match;
    vector< bool > used, vv;
    
    HopcroftKarp(int n, int m) : graph(n), match(m, -1), used(n) {}
    
    void add_edge(int u, int v) {
        graph[u].push_back(v);
    }
    
    void bfs() {
        dist.assign(graph.size(), -1);
        queue< int > que;
        for(int i = 0; i < graph.size(); i++) {
            if(!used[i]) {
                que.emplace(i);
                dist[i] = 0;
            }
        }
        
        while(!que.empty()) {
            int a = que.front();
            que.pop();
            for(auto &b : graph[a]) {
                int c = match[b];
                if(c >= 0 && dist[c] == -1) {
                    dist[c] = dist[a] + 1;
                    que.emplace(c);
                }
            }
        }
    }
    
    bool dfs(int a) {
        vv[a] = true;
        for(auto &b : graph[a]) {
            int c = match[b];
            if(c < 0 || (!vv[c] && dist[c] == dist[a] + 1 && dfs(c))) {
                match[b] = a;
                used[a] = true;
                return (true);
            }
        }
        return (false);
    }
    
    int bipartite_matching() {
        int ret = 0;
        while(true) {
            bfs();
            vv.assign(graph.size(), false);
            int flow = 0;
            for(int i = 0; i < graph.size(); i++) {
                if(!used[i] && dfs(i)) ++flow;
            }
            if(flow == 0) return (ret);
            ret += flow;
        }
    }
    
    void output() {
        for(int i = 0; i < match.size(); i++) {
            if(~match[i]) {
                cout << match[i] << "-" << i << endl;
            }
        }
    }
};

using mi = modint;
int n, m;
void output(vector<vector<int>>& v) {
    REP(i, n) {
        REP(j, m) {
            if(j) cout << " ";
            cout << v[i][j];
        }
        cout << endl;
    }
}

vector<vector<int>> func1(const vector<vector<int>>& a) {
    vector<vector<int>> b(n, vector<int>(m, -1));
    REP(i, n) {
        HopcroftKarp hk(m, m);
        vector<int> rev(m, -1);
        REP(j, n) {
            vector<int> v;
            REP(k, m) {
                if(b[j][k] == -1) v.pb(k);
            }
            REP(k, m) {
                if((a[j][k] - 1) / m == i) {
                    rev[(a[j][k] - 1) % m] = j;
                    REP(l, v.size()) {
                        hk.add_edge((a[j][k] - 1) % m, v[l]);
                    }
                }
            }
        }
        hk.bipartite_matching();
        REP(j, m) {
            b[rev[j]][hk.match[j]] = i * m + j + 1;
        }
    }
    return b;
}

vector<vector<int>> func2(const vector<vector<int>>& b) {
    vector<vector<int>> c(n, vector<int>(m));
    REP(i, m) {
        REP(j, n) {
            c[(b[j][i] - 1) / m][i] = b[j][i];
        }
    }
    return c;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> n >> m;
    vector<vector<int>> a(n, vector<int>(m));
    REP(i, n) REP(j, m) cin >> a[i][j];
    auto b = func1(a);
    output(b);
    auto c = func2(b);
    output(c);
    return 0;
}


Compiler output:
a.cc: In function 'std::vector<std::vector<int> > func1(const std::vector<std::vector<int> >&)':
a.cc:212:29: error: 'HopcroftKarp::HopcroftKarp(int, int)' is private within this context
  212 |         HopcroftKarp hk(m, m);
      |                             ^
a.cc:132:5: note: declared private here
  132 |     HopcroftKarp(int n, int m) : graph(n), match(m, -1), used(n) {}
      |     ^~~~~~~~~~~~
a.cc:223:36: error: 'void HopcroftKarp::add_edge(int, int)' is private within this context
  223 |                         hk.add_edge((a[j][k] - 1) % m, v[l]);
      |                         ~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
a.cc:134:10: note: declared private here
  134 |     void add_edge(int u, int v) {
      |          ^~~~~~~~
a.cc:228:30: error: 'int HopcroftKarp::bipartite_matching()' is private within this context
  228 |         hk.bipartite_matching();
      |         ~~~~~~~~~~~~~~~~~~~~~^~
a.cc:174:9: note: declared private here
  174 |     int bipartite_matching() {
      |         ^~~~~~~~~~~~~~~~~~
a.cc:230:26: error: 'std::vector<int> HopcroftKarp::match' is private within this context
  230 |             b[rev[j]][hk.match[j]] = i * m + j + 1;
      |                          ^~~~~
a.cc:129:25: note: declared private here
  129 |     vector< int > dist, match;
      |                         ^~~~~