結果
| 問題 | No.2263 Perms |
| ユーザー |
 maspy
|
| 提出日時 | 2023-04-07 22:52:26 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 5 ms / 2,000 ms |
| コード長 | 29,126 bytes |
| コンパイル時間 | 6,792 ms |
| コンパイル使用メモリ | 329,980 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2024-10-02 20:11:35 |
| 合計ジャッジ時間 | 7,184 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 1 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,248 KB |
| testcase_03 | AC | 1 ms
5,248 KB |
| testcase_04 | AC | 2 ms
5,248 KB |
| testcase_05 | AC | 2 ms
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| testcase_06 | AC | 4 ms
5,248 KB |
| testcase_07 | AC | 4 ms
5,248 KB |
| testcase_08 | AC | 3 ms
5,248 KB |
| testcase_09 | AC | 4 ms
5,248 KB |
| testcase_10 | AC | 1 ms
5,248 KB |
| testcase_11 | AC | 4 ms
5,248 KB |
| testcase_12 | AC | 4 ms
5,248 KB |
| testcase_13 | AC | 5 ms
5,248 KB |
| testcase_14 | AC | 5 ms
5,248 KB |
| testcase_15 | AC | 2 ms
5,248 KB |
| testcase_16 | AC | 2 ms
5,248 KB |
| testcase_17 | AC | 2 ms
5,248 KB |
| testcase_18 | AC | 2 ms
5,248 KB |
| testcase_19 | AC | 2 ms
5,248 KB |
| testcase_20 | AC | 4 ms
5,248 KB |
| testcase_21 | AC | 3 ms
5,248 KB |
| testcase_22 | AC | 3 ms
5,248 KB |
| testcase_23 | AC | 3 ms
5,248 KB |
| testcase_24 | AC | 2 ms
5,248 KB |
| testcase_25 | AC | 4 ms
5,248 KB |
| testcase_26 | AC | 4 ms
5,248 KB |
| testcase_27 | AC | 2 ms
5,248 KB |
| testcase_28 | AC | 2 ms
5,248 KB |
| testcase_29 | AC | 2 ms
5,248 KB |
| testcase_30 | AC | 1 ms
5,248 KB |
| testcase_31 | AC | 2 ms
5,248 KB |
| testcase_32 | AC | 2 ms
5,248 KB |
| testcase_33 | AC | 2 ms
5,248 KB |
| testcase_34 | AC | 1 ms
5,248 KB |
| testcase_35 | AC | 2 ms
5,248 KB |
| testcase_36 | AC | 2 ms
5,248 KB |
| testcase_37 | AC | 2 ms
5,248 KB |
| testcase_38 | AC | 3 ms
5,248 KB |
| testcase_39 | AC | 2 ms
5,248 KB |
| testcase_40 | AC | 1 ms
5,248 KB |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T, typename U>
T ceil(T x, U y) {
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sum = 0;
for (auto &&a: A) sum += a;
return sum;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
assert(!que.empty());
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
assert(!que.empty());
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>
namespace fastio {
#define FASTIO
// クラスが read(), print() を持っているかを判定するメタ関数
struct has_write_impl {
template <class T>
static auto check(T &&x) -> decltype(x.write(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) {
};
struct has_read_impl {
template <class T>
static auto check(T &&x) -> decltype(x.read(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {};
struct Scanner {
FILE *fp;
char line[(1 << 15) + 1];
size_t st = 0, ed = 0;
void reread() {
memmove(line, line + st, ed - st);
ed -= st;
st = 0;
ed += fread(line + ed, 1, (1 << 15) - ed, fp);
line[ed] = '\0';
}
bool succ() {
while (true) {
if (st == ed) {
reread();
if (st == ed) return false;
}
while (st != ed && isspace(line[st])) st++;
if (st != ed) break;
}
if (ed - st <= 50) {
bool sep = false;
for (size_t i = st; i < ed; i++) {
if (isspace(line[i])) {
sep = true;
break;
}
}
if (!sep) reread();
}
return true;
}
template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
bool read_single(T &ref) {
if (!succ()) return false;
while (true) {
size_t sz = 0;
while (st + sz < ed && !isspace(line[st + sz])) sz++;
ref.append(line + st, sz);
st += sz;
if (!sz || st != ed) break;
reread();
}
return true;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
bool read_single(T &ref) {
if (!succ()) return false;
bool neg = false;
if (line[st] == '-') {
neg = true;
st++;
}
ref = T(0);
while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
if (neg) ref = -ref;
return true;
}
template <typename T,
typename enable_if<has_read<T>::value>::type * = nullptr>
inline bool read_single(T &x) {
x.read();
return true;
}
bool read_single(double &ref) {
string s;
if (!read_single(s)) return false;
ref = std::stod(s);
return true;
}
bool read_single(char &ref) {
string s;
if (!read_single(s) || s.size() != 1) return false;
ref = s[0];
return true;
}
template <class T>
bool read_single(vector<T> &ref) {
for (auto &d: ref) {
if (!read_single(d)) return false;
}
return true;
}
template <class T, class U>
bool read_single(pair<T, U> &p) {
return (read_single(p.first) && read_single(p.second));
}
template <size_t N = 0, typename T>
void read_single_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
read_single(x);
read_single_tuple<N + 1>(t);
}
}
template <class... T>
bool read_single(tuple<T...> &tpl) {
read_single_tuple(tpl);
return true;
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
bool f = read_single(h);
assert(f);
read(t...);
}
Scanner(FILE *fp) : fp(fp) {}
};
struct Printer {
Printer(FILE *_fp) : fp(_fp) {}
~Printer() { flush(); }
static constexpr size_t SIZE = 1 << 15;
FILE *fp;
char line[SIZE], small[50];
size_t pos = 0;
void flush() {
fwrite(line, 1, pos, fp);
pos = 0;
}
void write(const char val) {
if (pos == SIZE) flush();
line[pos++] = val;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void write(T val) {
if (pos > (1 << 15) - 50) flush();
if (val == 0) {
write('0');
return;
}
if (val < 0) {
write('-');
val = -val; // todo min
}
size_t len = 0;
while (val) {
small[len++] = char(0x30 | (val % 10));
val /= 10;
}
for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
pos += len;
}
void write(const string s) {
for (char c: s) write(c);
}
void write(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) write(s[i]);
}
void write(const double x) {
ostringstream oss;
oss << fixed << setprecision(15) << x;
string s = oss.str();
write(s);
}
void write(const long double x) {
ostringstream oss;
oss << fixed << setprecision(15) << x;
string s = oss.str();
write(s);
}
template <typename T,
typename enable_if<has_write<T>::value>::type * = nullptr>
inline void write(T x) {
x.write();
}
template <class T>
void write(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write(' ');
write(val[i]);
}
}
template <class T, class U>
void write(const pair<T, U> val) {
write(val.first);
write(' ');
write(val.second);
}
template <size_t N = 0, typename T>
void write_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { write(' '); }
const auto x = std::get<N>(t);
write(x);
write_tuple<N + 1>(t);
}
}
template <class... T>
bool write(tuple<T...> tpl) {
write_tuple(tpl);
return true;
}
template <class T, size_t S>
void write(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write(' ');
write(val[i]);
}
}
void write(i128 val) {
string s;
bool negative = 0;
if (val < 0) {
negative = 1;
val = -val;
}
while (val) {
s += '0' + int(val % 10);
val /= 10;
}
if (negative) s += "-";
reverse(all(s));
if (len(s) == 0) s = "0";
write(s);
}
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
printer.write(head);
if (sizeof...(Tail)) printer.write(' ');
print(forward<Tail>(tail)...);
}
void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
scanner.read(head);
read(tail...);
}
} // namespace fastio
using fastio::print;
using fastio::flush;
using fastio::read;
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 2 "/home/maspy/compro/library/graph/bipartite_vertex_coloring.hpp"
#line 2 "/home/maspy/compro/library/graph/base.hpp"
template <typename T>
struct Edge {
int frm, to;
T cost;
int id;
};
template <typename T = int, bool directed = false>
struct Graph {
int N, M;
using cost_type = T;
using edge_type = Edge<T>;
vector<edge_type> edges;
vector<int> indptr;
vector<edge_type> csr_edges;
vc<int> vc_deg, vc_indeg, vc_outdeg;
bool prepared;
class OutgoingEdges {
public:
OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}
const edge_type* begin() const {
if (l == r) { return 0; }
return &G->csr_edges[l];
}
const edge_type* end() const {
if (l == r) { return 0; }
return &G->csr_edges[r];
}
private:
const Graph* G;
int l, r;
};
bool is_prepared() { return prepared; }
constexpr bool is_directed() { return directed; }
Graph() : N(0), M(0), prepared(0) {}
Graph(int N) : N(N), M(0), prepared(0) {}
void resize(int n) { N = n; }
void add(int frm, int to, T cost = 1, int i = -1) {
assert(!prepared);
assert(0 <= frm && 0 <= to && to < N);
if (i == -1) i = M;
auto e = edge_type({frm, to, cost, i});
edges.eb(e);
++M;
}
// wt, off
void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }
void read_graph(int M, bool wt = false, int off = 1) {
for (int m = 0; m < M; ++m) {
INT(a, b);
a -= off, b -= off;
if (!wt) {
add(a, b);
} else {
T c;
read(c);
add(a, b, c);
}
}
build();
}
void read_parent(int off = 1) {
for (int v = 1; v < N; ++v) {
INT(p);
p -= off;
add(p, v);
}
build();
}
void build() {
assert(!prepared);
prepared = true;
indptr.assign(N + 1, 0);
for (auto&& e: edges) {
indptr[e.frm + 1]++;
if (!directed) indptr[e.to + 1]++;
}
for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
auto counter = indptr;
csr_edges.resize(indptr.back() + 1);
for (auto&& e: edges) {
csr_edges[counter[e.frm]++] = e;
if (!directed)
csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
}
}
OutgoingEdges operator[](int v) const {
assert(prepared);
return {this, indptr[v], indptr[v + 1]};
}
vc<int> deg_array() {
if (vc_deg.empty()) calc_deg();
return vc_deg;
}
pair<vc<int>, vc<int>> deg_array_inout() {
if (vc_indeg.empty()) calc_deg_inout();
return {vc_indeg, vc_outdeg};
}
int deg(int v) {
if (vc_deg.empty()) calc_deg();
return vc_deg[v];
}
int in_deg(int v) {
if (vc_indeg.empty()) calc_deg_inout();
return vc_indeg[v];
}
int out_deg(int v) {
if (vc_outdeg.empty()) calc_deg_inout();
return vc_outdeg[v];
}
void debug() {
print("Graph");
if (!prepared) {
print("frm to cost id");
for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
} else {
print("indptr", indptr);
print("frm to cost id");
FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
}
}
// G における頂点 V[i] が、新しいグラフで i になるようにする
Graph<T, directed> rearrange(vc<int> V) {
int n = len(V);
map<int, int> MP;
FOR(i, n) MP[V[i]] = i;
Graph<T, directed> G(n);
for (auto&& e: edges) {
if (MP.count(e.frm) && MP.count(e.to)) {
G.add(MP[e.frm], MP[e.to], e.cost);
}
}
G.build();
return G;
}
private:
void calc_deg() {
assert(vc_deg.empty());
vc_deg.resize(N);
for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
}
void calc_deg_inout() {
assert(vc_indeg.empty());
vc_indeg.resize(N);
vc_outdeg.resize(N);
for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
}
};
#line 2 "/home/maspy/compro/library/ds/unionfind/unionfind.hpp"
struct UnionFind {
int n, n_comp;
vc<int> dat; // par or (-size)
UnionFind(int n = 0) { build(n); }
void build(int m) {
n = m, n_comp = m;
dat.assign(n, -1);
}
void reset() { build(n); }
int operator[](int x) {
while (dat[x] >= 0) {
int pp = dat[dat[x]];
if (pp < 0) { return dat[x]; }
x = dat[x] = pp;
}
return x;
}
ll size(int x) {
assert(dat[x] < 0);
return -dat[x];
}
bool merge(int x, int y) {
x = (*this)[x], y = (*this)[y];
if (x == y) return false;
if (-dat[x] < -dat[y]) swap(x, y);
dat[x] += dat[y], dat[y] = x, n_comp--;
return true;
}
};
#line 5 "/home/maspy/compro/library/graph/bipartite_vertex_coloring.hpp"
// 二部グラフでなかった場合には empty
template <typename Graph>
vc<int> bipartite_vertex_coloring(Graph& G) {
assert(G.is_prepared());
int n = G.N;
UnionFind uf(2 * n);
for (auto&& e: G.edges) {
int u = e.frm, v = e.to;
if (e.cost == 0) uf.merge(u, v), uf.merge(u + n, v + n);
if (e.cost != 0) uf.merge(u + n, v), uf.merge(u, v + n);
}
vc<int> color(2 * n, -1);
FOR(v, n) if (uf[v] == v && color[uf[v]] < 0) {
color[uf[v]] = 0;
color[uf[v + n]] = 1;
}
FOR(v, n) color[v] = color[uf[v]];
color.resize(n);
FOR(v, n) if (uf[v] == uf[v + n]) return {};
return color;
}
#line 3 "/home/maspy/compro/library/graph/strongly_connected_component.hpp"
template <typename Graph>
pair<int, vc<int>> strongly_connected_component(Graph& G) {
assert(G.is_directed());
assert(G.is_prepared());
int N = G.N;
int C = 0;
vc<int> comp(N);
vc<int> low(N);
vc<int> ord(N, -1);
vc<int> visited;
int now = 0;
auto dfs = [&](auto self, int v) -> void {
low[v] = now;
ord[v] = now;
++now;
visited.eb(v);
for (auto&& [frm, to, cost, id]: G[v]) {
if (ord[to] == -1) {
self(self, to);
chmin(low[v], low[to]);
} else {
chmin(low[v], ord[to]);
}
}
if (low[v] == ord[v]) {
while (1) {
int u = visited.back();
visited.pop_back();
ord[u] = N;
comp[u] = C;
if (u == v) break;
}
++C;
}
};
FOR(v, N) {
if (ord[v] == -1) dfs(dfs, v);
}
FOR(v, N) comp[v] = C - 1 - comp[v];
return {C, comp};
}
template <typename GT>
Graph<int, 1> scc_dag(GT& G, int C, vc<int>& comp) {
Graph<int, 1> DAG(C);
vvc<int> edges(C);
for (auto&& e: G.edges) {
int x = comp[e.frm], y = comp[e.to];
if (x == y) continue;
edges[x].eb(y);
}
FOR(c, C) {
UNIQUE(edges[c]);
for (auto&& to: edges[c]) DAG.add(c, to);
}
DAG.build();
return DAG;
}
#line 4 "/home/maspy/compro/library/flow/bipartite.hpp"
template <typename GT>
struct BipartiteMatching {
int N;
GT& G;
vc<int> color;
vc<int> dist, match;
vc<int> vis;
BipartiteMatching(GT& G) : N(G.N), G(G), dist(G.N, -1), match(G.N, -1) {
color = bipartite_vertex_coloring(G);
assert(!color.empty());
while (1) {
bfs();
vis.assign(N, false);
int flow = 0;
FOR(v, N) if (!color[v] && match[v] == -1 && dfs(v))++ flow;
if (!flow) break;
}
}
BipartiteMatching(GT& G, vc<int> color)
: N(G.N), G(G), color(color), dist(G.N, -1), match(G.N, -1) {
while (1) {
bfs();
vis.assign(N, false);
int flow = 0;
FOR(v, N) if (!color[v] && match[v] == -1 && dfs(v))++ flow;
if (!flow) break;
}
}
void bfs() {
dist.assign(N, -1);
queue<int> que;
FOR(v, N) if (!color[v] && match[v] == -1) que.emplace(v), dist[v] = 0;
while (!que.empty()) {
int v = que.front();
que.pop();
for (auto&& e: G[v]) {
dist[e.to] = 0;
int w = match[e.to];
if (w != -1 && dist[w] == -1) dist[w] = dist[v] + 1, que.emplace(w);
}
}
}
bool dfs(int v) {
vis[v] = 1;
for (auto&& e: G[v]) {
int w = match[e.to];
if (w == -1 || (!vis[w] && dist[w] == dist[v] + 1 && dfs(w))) {
match[e.to] = v, match[v] = e.to;
return true;
}
}
return false;
}
vc<pair<int, int>> matching() {
vc<pair<int, int>> res;
FOR(v, N) if (v < match[v]) res.eb(v, match[v]);
return res;
}
vc<int> vertex_cover() {
vc<int> res;
FOR(v, N) if (color[v] ^ (dist[v] == -1)) { res.eb(v); }
return res;
}
vc<int> independent_set() {
vc<int> res;
FOR(v, N) if (!(color[v] ^ (dist[v] == -1))) { res.eb(v); }
return res;
}
vc<int> edge_cover() {
vc<bool> done(N);
vc<int> res;
for (auto&& e: G.edges) {
if (done[e.frm] || done[e.to]) continue;
if (match[e.frm] == e.to) {
res.eb(e.id);
done[e.frm] = done[e.to] = 1;
}
}
for (auto&& e: G.edges) {
if (!done[e.frm]) {
res.eb(e.id);
done[e.frm] = 1;
}
if (!done[e.to]) {
res.eb(e.id);
done[e.to] = 1;
}
}
sort(all(res));
return res;
}
/* Dulmage–Mendelsohn decomposition
https://en.wikipedia.org/wiki/Dulmage%E2%80%93Mendelsohn_decomposition
http://www.misojiro.t.u-tokyo.ac.jp/~murota/lect-ouyousurigaku/dm050410.pdf
https://hitonanode.github.io/cplib-cpp/graph/dulmage_mendelsohn_decomposition.hpp.html
- 最大マッチングとしてありうる iff 同じ W を持つ
- 辺 uv が必ず使われる：同じ W を持つ辺が唯一
- color=0 から 1 への辺：W[l] <= W[r]
- color=0 の点が必ず使われる：W=1,2,...,K
- color=1 の点が必ず使われる：W=0,1,...,K-1
*/
pair<int, vc<int>> DM_decomposition() {
// 非飽和点からの探索
vc<int> W(N, -1);
vc<int> que;
auto add = [&](int v, int x) -> void {
if (W[v] == -1) {
W[v] = x;
que.eb(v);
}
};
FOR(v, N) if (match[v] == -1 && color[v] == 0) add(v, 0);
FOR(v, N) if (match[v] == -1 && color[v] == 1) add(v, infty<int>);
while (len(que)) {
auto v = POP(que);
if (match[v] != -1) add(match[v], W[v]);
if (color[v] == 0 && W[v] == 0) {
for (auto&& e: G[v]) { add(e.to, W[v]); }
}
if (color[v] == 1 && W[v] == infty<int>) {
for (auto&& e: G[v]) { add(e.to, W[v]); }
}
}
// 残った点からなるグラフを作って強連結成分分解
vc<int> V;
FOR(v, N) if (W[v] == -1) V.eb(v);
int n = len(V);
Graph<bool, 1> DG(n);
FOR(i, n) {
int v = V[i];
if (match[v] != -1) {
int j = LB(V, match[v]);
DG.add(i, j);
}
if (color[v] == 0) {
for (auto&& e: G[v]) {
if (W[e.to] != -1 || e.to == match[v]) continue;
int j = LB(V, e.to);
DG.add(i, j);
}
}
}
DG.build();
auto [K, comp] = strongly_connected_component(DG);
K += 1;
// 答
FOR(i, n) { W[V[i]] = 1 + comp[i]; }
FOR(v, N) if (W[v] == infty<int>) W[v] = K;
return {K, W};
}
void debug() {
print("match", match);
print("min vertex covor", vertex_cover());
print("max indep set", independent_set());
print("min edge cover", edge_cover());
}
};
#line 4 "/home/maspy/compro/library/graph/bipartite_edge_coloring.hpp"
struct RegularBipartiteColoring {
using P = pair<int, int>;
int N, M;
vc<P> edges;
vvc<int> solve(int n, int k, vc<P> G) {
N = n;
M = len(G);
edges = G;
vc<int> A(M);
iota(all(A), 0);
return solve_inner(M / N, A);
}
vvc<int> solve_inner(int k, vc<int> A) {
return (k % 2 == 0 ? solve_even(k, A) : solve_odd(k, A));
}
vvc<int> solve_even(int k, vc<int> A) {
assert(k % 2 == 0);
if (k == 0) return {};
// 2^m <= k < 2^{m+1}
int m = 0;
while (1 << (m + 1) <= k) ++m;
vvc<int> res;
if (k != 1 << m) {
auto [B, C] = split(k, A);
auto dat = solve_inner(k / 2, C);
FOR(j, k - (1 << m)) { res.eb(dat[j]); }
FOR(j, k - (1 << m), len(dat)) {
for (auto&& idx: dat[j]) B.eb(idx);
}
k = 1 << m;
swap(A, B);
}
auto dfs = [&](auto& dfs, int K, vc<int> A) -> void {
if (K == 1) {
res.eb(A);
return;
}
auto [B, C] = split(k, A);
dfs(dfs, K / 2, B);
dfs(dfs, K / 2, C);
};
dfs(dfs, k, A);
return res;
}
vvc<int> solve_odd(int k, vc<int> A) {
assert(k % 2 == 1);
if (k == 1) { return {A}; }
vc<bool> match = matching(k, A);
vc<int> B;
B.reserve(len(A) - N);
vc<int> es;
FOR(i, len(A)) {
if (match[i]) es.eb(A[i]);
if (!match[i]) B.eb(A[i]);
}
vvc<int> res = solve_inner(k - 1, B);
res.eb(es);
return res;
}
vc<bool> matching(int k, vc<int> A) {
Graph<bool, 0> G(N + N);
vc<int> color(N + N);
FOR(v, N) color[v] = 0;
for (auto&& eid: A) {
auto [a, b] = edges[eid];
G.add(a, b);
}
G.build();
BipartiteMatching<decltype(G)> BM(G);
auto& match = BM.match;
vc<bool> res(len(A));
FOR(i, len(A)) {
auto idx = A[i];
auto [a, b] = edges[idx];
if (match[a] == b) {
match[a] = -1;
res[i] = 1;
}
}
return res;
}
pair<vc<int>, vc<int>> split(int k, vc<int> A) {
assert(k % 2 == 0);
// 2 つの k/2 - regular に分割する。
int n = len(A);
vc<bool> rest(n);
vc<int> A0, A1;
A0.reserve(n / 2), A1.reserve(n / 2);
vvc<P> G(N + N);
FOR(i, n) {
rest[i] = 1;
auto [a, b] = edges[A[i]];
G[a].eb(i, b);
G[b].eb(i, a);
}
auto dfs = [&](auto& dfs, int v, int color) -> void {
while (len(G[v])) {
auto [i, to] = POP(G[v]);
if (!rest[i]) continue;
rest[i] = 0;
if (color == 0) A0.eb(A[i]);
if (color == 1) A1.eb(A[i]);
dfs(dfs, to, 1 ^ color);
}
};
FOR(v, N) dfs(dfs, v, 0);
return {A0, A1};
}
};
template <typename GT>
pair<int, vc<int>> bipartite_edge_coloring(GT& G) {
auto vcolor = bipartite_vertex_coloring<decltype(G)>(G);
auto deg = G.deg_array();
int D = MAX(deg);
UnionFind uf(G.N);
FOR(c, 2) {
pqg<pair<int, int>> que;
FOR(v, G.N) {
if (vcolor[v] == c) que.emplace(deg[v], v);
}
while (len(que) > 1) {
auto [d1, v1] = POP(que);
auto [d2, v2] = POP(que);
if (d1 + d2 > D) break;
uf.merge(v1, v2);
int r = uf[v1];
que.emplace(d1 + d2, r);
}
}
vc<int> LV, RV;
FOR(v, G.N) if (uf[v] == v) {
if (vcolor[v] == 0) LV.eb(v);
if (vcolor[v] == 1) RV.eb(v);
}
int X = max(len(LV), len(RV));
vc<int> degL(X), degR(X);
vc<pair<int, int>> edges;
for (auto&& e: G.edges) {
int a = e.frm, b = e.to;
a = uf[a], b = uf[b];
a = LB(LV, a);
b = LB(RV, b);
degL[a]++, degR[b]++;
edges.eb(a, X + b);
}
int p = 0, q = 0;
while (p < X && q < X) {
if (degL[p] == D) {
++p;
continue;
}
if (degR[q] == D) {
++q;
continue;
}
edges.eb(p, X + q);
degL[p]++, degR[q]++;
}
RegularBipartiteColoring RBC;
vvc<int> res = RBC.solve(X, D, edges);
vc<int> ecolor(len(edges));
FOR(i, len(res)) {
for (auto&& j: res[i]) ecolor[j] = i;
}
ecolor.resize(G.M);
return {D, ecolor};
}
#line 4 "main.cpp"
void solve() {
LL(N, M);
VV(int, A, N, N);
FOR(i, N) {
ll x = 0;
FOR(j, N) x += A[i][j];
if (x != M) return print(-1);
}
FOR(j, N) {
ll x = 0;
FOR(i, N) x += A[i][j];
if (x != M) return print(-1);
}
Graph<bool, 0> G(N + N);
FOR(i, N) FOR(j, N) {
int x = A[i][j];
FOR(x) G.add(i, N + j);
}
G.build();
auto [nc, color] = bipartite_edge_coloring<decltype(G)>(G);
vv(int, ANS, M, N);
FOR(e, G.M) {
int m = color[e];
int a = G.edges[e].frm;
int b = G.edges[e].to;
b -= N;
ANS[m][a] = 1 + b;
}
FOR(m, M) print(ANS[m]);
}
signed main() {
int T = 1;
// INT(T);
FOR(T) solve();
return 0;
}