結果
| 問題 | No.2263 Perms |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2023-04-07 22:26:43 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 5 ms / 2,000 ms |
| コード長 | 38,305 bytes |
| コンパイル時間 | 3,708 ms |
| コンパイル使用メモリ | 244,552 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2024-10-02 19:54:44 |
| 合計ジャッジ時間 | 4,989 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 | 2 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,248 KB |
| testcase_03 | AC | 2 ms
5,248 KB |
| testcase_04 | AC | 2 ms
5,248 KB |
| testcase_05 | AC | 2 ms
5,248 KB |
| testcase_06 | AC | 5 ms
5,248 KB |
| testcase_07 | AC | 4 ms
5,248 KB |
| testcase_08 | AC | 4 ms
5,248 KB |
| testcase_09 | AC | 4 ms
5,248 KB |
| testcase_10 | AC | 2 ms
5,248 KB |
| testcase_11 | AC | 5 ms
5,248 KB |
| testcase_12 | AC | 4 ms
5,248 KB |
| testcase_13 | AC | 4 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 | 4 ms
5,248 KB |
| testcase_22 | AC | 4 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 | 2 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 | 2 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 | 2 ms
5,248 KB |
ソースコード
#include <bits/stdc++.h>
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using f64 = double;
using f80 = long double;
using f128 = __float128;
constexpr i32 operator"" _i32(u64 v) { return v; }
constexpr u32 operator"" _u32(u64 v) { return v; }
constexpr i64 operator"" _i64(u64 v) { return v; }
constexpr u64 operator"" _u64(u64 v) { return v; }
constexpr f64 operator"" _f64(f80 v) { return v; }
constexpr f80 operator"" _f80(f80 v) { return v; }
using Istream = std::istream;
using Ostream = std::ostream;
using Str = std::string;
template<typename T>
using Lt = std::less<T>;
template<typename T>
using Gt = std::greater<T>;
template<int n>
using BSet = std::bitset<n>;
template<typename T1, typename T2>
using Pair = std::pair<T1, T2>;
template<typename... Ts>
using Tup = std::tuple<Ts...>;
template<typename T, int N>
using Arr = std::array<T, N>;
template<typename... Ts>
using Deq = std::deque<Ts...>;
template<typename... Ts>
using Set = std::set<Ts...>;
template<typename... Ts>
using MSet = std::multiset<Ts...>;
template<typename... Ts>
using USet = std::unordered_set<Ts...>;
template<typename... Ts>
using UMSet = std::unordered_multiset<Ts...>;
template<typename... Ts>
using Map = std::map<Ts...>;
template<typename... Ts>
using MMap = std::multimap<Ts...>;
template<typename... Ts>
using UMap = std::unordered_map<Ts...>;
template<typename... Ts>
using UMMap = std::unordered_multimap<Ts...>;
template<typename... Ts>
using Vec = std::vector<Ts...>;
template<typename... Ts>
using Stack = std::stack<Ts...>;
template<typename... Ts>
using Queue = std::queue<Ts...>;
template<typename T>
using MaxHeap = std::priority_queue<T>;
template<typename T>
using MinHeap = std::priority_queue<T, Vec<T>, Gt<T>>;
constexpr bool LOCAL = false;
constexpr bool OJ = not LOCAL;
template<typename T>
static constexpr T OjLocal(T oj, T local)
{
return LOCAL ? local : oj;
}
template<typename T>
constexpr T LIMMIN = std::numeric_limits<T>::min();
template<typename T>
constexpr T LIMMAX = std::numeric_limits<T>::max();
template<typename T>
constexpr T INF = (LIMMAX<T> - 1) / 2;
template<typename T>
constexpr T PI = T{3.141592653589793238462643383279502884};
template<typename T = u64>
constexpr T TEN(int n)
{
return n == 0 ? T{1} : TEN<T>(n - 1) * T{10};
}
template<typename T>
constexpr bool chmin(T& a, const T& b)
{
return (a > b ? (a = b, true) : false);
}
template<typename T>
constexpr bool chmax(T& a, const T& b)
{
return (a < b ? (a = b, true) : false);
}
template<typename T>
constexpr T floorDiv(T x, T y)
{
assert(y != 0);
if (y < 0) { x = -x, y = -y; }
return x >= 0 ? x / y : (x - y + 1) / y;
}
template<typename T>
constexpr T ceilDiv(T x, T y)
{
assert(y != 0);
if (y < 0) { x = -x, y = -y; }
return x >= 0 ? (x + y - 1) / y : x / y;
}
template<typename T, typename I>
constexpr T powerMonoid(T v, I n, const T& e)
{
assert(n >= 0);
if (n == 0) { return e; }
return (n % 2 == 1 ? v * powerMonoid(v, n - 1, e) : powerMonoid(v * v, n / 2, e));
}
template<typename T, typename I>
constexpr T powerInt(T v, I n)
{
return powerMonoid(v, n, T{1});
}
template<typename Vs, typename V>
constexpr void fillAll(Vs& arr, const V& v)
{
if constexpr (std::is_convertible<V, Vs>::value) {
arr = v;
} else {
for (auto& subarr : arr) { fillAll(subarr, v); }
}
}
template<typename Vs>
constexpr void sortAll(Vs& vs)
{
std::sort(std::begin(vs), std::end(vs));
}
template<typename Vs, typename C>
constexpr void sortAll(Vs& vs, C comp)
{
std::sort(std::begin(vs), std::end(vs), comp);
}
template<typename Vs>
constexpr void reverseAll(Vs& vs)
{
std::reverse(std::begin(vs), std::end(vs));
}
template<typename Vs>
constexpr Vs reversed(const Vs& vs)
{
auto rvs = vs;
reverseAll(rvs);
return rvs;
}
template<typename V, typename Vs>
constexpr V sumAll(const Vs& vs)
{
if constexpr (std::is_convertible<Vs, V>::value) {
return static_cast<V>(vs);
} else {
V ans = 0;
for (const auto& v : vs) { ans += sumAll<V>(v); }
return ans;
}
}
template<typename Vs>
constexpr int minInd(const Vs& vs)
{
return std::min_element(std::begin(vs), std::end(vs)) - std::begin(vs);
}
template<typename Vs>
constexpr int maxInd(const Vs& vs)
{
return std::max_element(std::begin(vs), std::end(vs)) - std::begin(vs);
}
template<typename Vs, typename V>
constexpr int lbInd(const Vs& vs, const V& v)
{
return std::lower_bound(std::begin(vs), std::end(vs), v) - std::begin(vs);
}
template<typename Vs, typename V>
constexpr int ubInd(const Vs& vs, const V& v)
{
return std::upper_bound(std::begin(vs), std::end(vs), v) - std::begin(vs);
}
template<typename Vs, typename V>
constexpr void plusAll(Vs& vs, const V& v)
{
for (auto& v_ : vs) { v_ += v; }
}
template<typename Vs>
constexpr void concat(Vs& vs1, const Vs& vs2)
{
std::copy(std::begin(vs2), std::end(vs2), std::back_inserter(vs1));
}
template<typename Vs>
constexpr void concatted(const Vs& vs1, const Vs& vs2)
{
auto vs = vs1;
concat(vs, vs2);
return vs;
}
template<typename T, typename F>
constexpr Vec<T> genVec(int n, F gen)
{
Vec<T> ans;
std::generate_n(std::back_inserter(ans), n, gen);
return ans;
}
template<typename T = int>
constexpr Vec<T> iotaVec(int n, T offset = 0)
{
Vec<T> ans(n);
std::iota(std::begin(ans), std::end(ans), offset);
return ans;
}
template<typename Vs>
constexpr void rearrange(Vs& vs, const Vec<int>& is)
{
auto vs_ = vs;
for (int i = 0; i < (int)is.size(); i++) { vs[i] = vs_[is[i]]; }
}
inline Vec<int> reversePerm(const Vec<int>& is)
{
auto ris = is;
for (int i = 0; i < (int)is.size(); i++) { ris[is[i]] = i; }
return ris;
}
inline Ostream& operator<<(Ostream& os, i128 v)
{
bool minus = false;
if (v < 0) { minus = true, v = -v; }
Str ans;
if (v == 0) { ans = "0"; }
while (v) { ans.push_back('0' + v % 10), v /= 10; }
std::reverse(ans.begin(), ans.end());
return os << (minus ? "-" : "") << ans;
}
inline Ostream& operator<<(Ostream& os, u128 v)
{
Str ans;
if (v == 0) { ans = "0"; }
while (v) { ans.push_back('0' + v % 10), v /= 10; }
std::reverse(ans.begin(), ans.end());
return os << ans;
}
constexpr int popCount(u64 v) { return v ? __builtin_popcountll(v) : 0; }
constexpr int topBit(u64 v) { return v == 0 ? -1 : 63 - __builtin_clzll(v); }
constexpr int lowBit(u64 v) { return v == 0 ? 64 : __builtin_ctzll(v); }
constexpr int bitWidth(u64 v) { return topBit(v) + 1; }
constexpr u64 bitCeil(u64 v) { return v ? (1_u64 << bitWidth(v - 1)) : 1_u64; }
constexpr u64 bitFloor(u64 v) { return v ? (1_u64 << topBit(v)) : 0_u64; }
constexpr bool hasSingleBit(u64 v) { return (v > 0) and ((v & (v - 1)) == 0); }
constexpr bool isBitOn(u64 mask, int ind) { return (mask >> ind) & 1_u64; }
constexpr bool isBitOff(u64 mask, int ind) { return not isBitOn(mask, ind); }
constexpr u64 bitMask(int bitWidth) { return (bitWidth == 64 ? ~0_u64 : (1_u64 << bitWidth) - 1); }
constexpr u64 bitMask(int start, int end) { return bitMask(end - start) << start; }
template<typename F>
struct Fix : F
{
constexpr Fix(F&& f) : F{std::forward<F>(f)} {}
template<typename... Args>
constexpr auto operator()(Args&&... args) const
{
return F::operator()(*this, std::forward<Args>(args)...);
}
};
class irange
{
private:
struct itr
{
constexpr itr(i64 start = 0, i64 step = 1) : m_cnt{start}, m_step{step} {}
constexpr bool operator!=(const itr& it) const { return m_cnt != it.m_cnt; }
constexpr i64 operator*() { return m_cnt; }
constexpr itr& operator++() { return m_cnt += m_step, *this; }
i64 m_cnt, m_step;
};
i64 m_start, m_end, m_step;
public:
static constexpr i64 cnt(i64 start, i64 end, i64 step)
{
if (step == 0) { return -1; }
const i64 d = (step > 0 ? step : -step);
const i64 l = (step > 0 ? start : end);
const i64 r = (step > 0 ? end : start);
i64 n = (r - l) / d + ((r - l) % d ? 1 : 0);
if (l >= r) { n = 0; }
return n;
}
constexpr irange(i64 start, i64 end, i64 step = 1)
: m_start{start}, m_end{m_start + step * cnt(start, end, step)}, m_step{step}
{
assert(step != 0);
}
constexpr itr begin() const { return itr{m_start, m_step}; }
constexpr itr end() const { return itr{m_end, m_step}; }
};
constexpr irange rep(i64 end) { return irange(0, end, 1); }
constexpr irange per(i64 rend) { return irange(rend - 1, -1, -1); }
class Scanner
{
public:
Scanner(Istream& is = std::cin) : m_is{is} { m_is.tie(nullptr)->sync_with_stdio(false); }
template<typename T>
T val()
{
T v;
return m_is >> v, v;
}
template<typename T>
T val(T offset)
{
return val<T>() - offset;
}
template<typename T>
Vec<T> vec(int n)
{
return genVec<T>(n, [&]() { return val<T>(); });
}
template<typename T>
Vec<T> vec(int n, T offset)
{
return genVec<T>(n, [&]() { return val<T>(offset); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m)
{
return genVec<Vec<T>>(n, [&]() { return vec<T>(m); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m, const T offset)
{
return genVec<Vec<T>>(n, [&]() { return vec<T>(m, offset); });
}
template<typename... Args>
auto tup()
{
return Tup<Args...>{val<Args>()...};
}
template<typename... Args>
auto tup(const Args&... offsets)
{
return Tup<Args...>{val<Args>(offsets)...};
}
private:
Istream& m_is;
};
inline Scanner in;
class Printer
{
public:
Printer(Ostream& os = std::cout) : m_os{os} { m_os << std::fixed << std::setprecision(15); }
template<typename... Args>
int operator()(const Args&... args)
{
return dump(args...), 0;
}
template<typename... Args>
int ln(const Args&... args)
{
return dump(args...), m_os << '\n', 0;
}
template<typename... Args>
int el(const Args&... args)
{
return dump(args...), m_os << std::endl, 0;
}
int YES(bool b = true) { return ln(b ? "YES" : "NO"); }
int NO(bool b = true) { return YES(not b); }
int Yes(bool b = true) { return ln(b ? "Yes" : "No"); }
int No(bool b = true) { return Yes(not b); }
private:
template<typename T>
void dump(const T& v)
{
m_os << v;
}
template<typename T>
void dump(const Vec<T>& vs)
{
for (int i : rep(vs.size())) { m_os << (i ? " " : ""), dump(vs[i]); }
}
template<typename T>
void dump(const Vec<Vec<T>>& vss)
{
for (int i : rep(vss.size())) { m_os << (i ? "\n" : ""), dump(vss[i]); }
}
template<typename T, typename... Ts>
int dump(const T& v, const Ts&... args)
{
return dump(v), m_os << ' ', dump(args...), 0;
}
Ostream& m_os;
};
inline Printer out;
template<typename T, int n, int i = 0>
auto ndVec(int const (&szs)[n], const T x = T{})
{
if constexpr (i == n) {
return x;
} else {
return std::vector(szs[i], ndVec<T, n, i + 1>(szs, x));
}
}
template<typename T, typename F>
inline T binSearch(T ng, T ok, F check)
{
while (std::abs(ok - ng) > 1) {
const T mid = (ok + ng) / 2;
(check(mid) ? ok : ng) = mid;
}
return ok;
}
template<typename T>
constexpr Pair<T, T> extgcd(const T a, const T b) // [x,y] -> ax+by=gcd(a,b)
{
static_assert(std::is_signed_v<T>, "Signed integer is allowed.");
assert(a != 0 or b != 0);
if (a >= 0 and b >= 0) {
if (a < b) {
const auto [y, x] = extgcd(b, a);
return {x, y};
}
if (b == 0) { return {1, 0}; }
const auto [x, y] = extgcd(b, a % b);
return {y, x - (a / b) * y};
} else {
auto [x, y] = extgcd(std::abs(a), std::abs(b));
if (a < 0) { x = -x; }
if (b < 0) { y = -y; }
return {x, y};
}
}
template<typename T>
constexpr T inverse(const T a, const T mod) // ax=gcd(a,M) (mod M)
{
assert(a > 0 and mod > 0);
auto [x, y] = extgcd(a, mod);
if (x <= 0) { x += mod; }
return x;
}
template<u32 mod_, u32 root_, u32 max2p_>
class modint
{
template<typename U = u32&>
static U modRef()
{
static u32 s_mod = 0;
return s_mod;
}
template<typename U = u32&>
static U rootRef()
{
static u32 s_root = 0;
return s_root;
}
template<typename U = u32&>
static U max2pRef()
{
static u32 s_max2p = 0;
return s_max2p;
}
public:
static_assert(mod_ <= LIMMAX<i32>, "mod(signed int size) only supported!");
static constexpr bool isDynamic() { return (mod_ == 0); }
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> mod()
{
return mod_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> mod()
{
return modRef();
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> root()
{
return root_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> root()
{
return rootRef();
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> max2p()
{
return max2p_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> max2p()
{
return max2pRef();
}
template<typename U = u32>
static void setMod(std::enable_if_t<mod_ == 0, U> m)
{
assert(1 <= m and m <= LIMMAX<i32>);
modRef() = m;
sinvRef() = {1, 1};
factRef() = {1, 1};
ifactRef() = {1, 1};
}
template<typename U = u32>
static void setRoot(std::enable_if_t<mod_ == 0, U> r)
{
rootRef() = r;
}
template<typename U = u32>
static void setMax2p(std::enable_if_t<mod_ == 0, U> m)
{
max2pRef() = m;
}
constexpr modint() : m_val{0} {}
constexpr modint(i64 v) : m_val{normll(v)} {}
constexpr void setRaw(u32 v) { m_val = v; }
constexpr modint operator-() const { return modint{0} - (*this); }
constexpr modint& operator+=(const modint& m)
{
m_val = norm(m_val + m.val());
return *this;
}
constexpr modint& operator-=(const modint& m)
{
m_val = norm(m_val + mod() - m.val());
return *this;
}
constexpr modint& operator*=(const modint& m)
{
m_val = normll((i64)m_val * (i64)m.val() % (i64)mod());
return *this;
}
constexpr modint& operator/=(const modint& m) { return *this *= m.inv(); }
constexpr modint operator+(const modint& m) const
{
auto v = *this;
return v += m;
}
constexpr modint operator-(const modint& m) const
{
auto v = *this;
return v -= m;
}
constexpr modint operator*(const modint& m) const
{
auto v = *this;
return v *= m;
}
constexpr modint operator/(const modint& m) const
{
auto v = *this;
return v /= m;
}
constexpr bool operator==(const modint& m) const { return m_val == m.val(); }
constexpr bool operator!=(const modint& m) const { return not(*this == m); }
friend Istream& operator>>(Istream& is, modint& m)
{
i64 v;
return is >> v, m = v, is;
}
friend Ostream& operator<<(Ostream& os, const modint& m) { return os << m.val(); }
constexpr u32 val() const { return m_val; }
template<typename I>
constexpr modint pow(I n) const
{
return powerInt(*this, n);
}
constexpr modint inv() const { return inverse<i32>(m_val, mod()); }
static modint sinv(u32 n)
{
auto& is = sinvRef();
for (u32 i = (u32)is.size(); i <= n; i++) { is.push_back(-is[mod() % i] * (mod() / i)); }
return is[n];
}
static modint fact(u32 n)
{
auto& fs = factRef();
for (u32 i = (u32)fs.size(); i <= n; i++) { fs.push_back(fs.back() * i); }
return fs[n];
}
static modint ifact(u32 n)
{
auto& ifs = ifactRef();
for (u32 i = (u32)ifs.size(); i <= n; i++) { ifs.push_back(ifs.back() * sinv(i)); }
return ifs[n];
}
static modint perm(int n, int k) { return k > n or k < 0 ? modint{0} : fact(n) * ifact(n - k); }
static modint comb(int n, int k)
{
return k > n or k < 0 ? modint{0} : fact(n) * ifact(n - k) * ifact(k);
}
private:
static Vec<modint>& sinvRef()
{
static Vec<modint> is{1, 1};
return is;
}
static Vec<modint>& factRef()
{
static Vec<modint> fs{1, 1};
return fs;
}
static Vec<modint>& ifactRef()
{
static Vec<modint> ifs{1, 1};
return ifs;
}
static constexpr u32 norm(u32 x) { return x < mod() ? x : x - mod(); }
static constexpr u32 normll(i64 x) { return norm(u32(x % (i64)mod() + (i64)mod())); }
u32 m_val;
};
using modint_1000000007 = modint<1000000007, 5, 1>;
using modint_998244353 = modint<998244353, 3, 23>;
template<int id>
using modint_dynamic = modint<0, 0, id>;
template<typename T = int>
class Graph
{
struct Edge
{
Edge() = default;
Edge(int i, int t, T c) : id{i}, to{t}, cost{c} {}
int id;
int to;
T cost;
operator int() const { return to; }
};
public:
Graph(int n) : m_v{n}, m_edges(n) {}
void addEdge(int u, int v, bool bi = false)
{
assert(0 <= u and u < m_v);
assert(0 <= v and v < m_v);
m_edges[u].emplace_back(m_e, v, 1);
if (bi) { m_edges[v].emplace_back(m_e, u, 1); }
m_e++;
}
void addEdge(int u, int v, const T& c, bool bi = false)
{
assert(0 <= u and u < m_v);
assert(0 <= v and v < m_v);
m_edges[u].emplace_back(m_e, v, c);
if (bi) { m_edges[v].emplace_back(m_e, u, c); }
m_e++;
}
const Vec<Edge>& operator[](const int u) const
{
assert(0 <= u and u < m_v);
return m_edges[u];
}
Vec<Edge>& operator[](const int u)
{
assert(0 <= u and u < m_v);
return m_edges[u];
}
int v() const { return m_v; }
int e() const { return m_e; }
friend Ostream& operator<<(Ostream& os, const Graph& g)
{
for (int u : rep(g.v())) {
for (const auto& [id, v, c] : g[u]) {
os << "[" << id << "]: ";
os << u << "->" << v << "(" << c << ")\n";
}
}
return os;
}
Vec<T> sizes(int root = 0) const
{
const int N = v();
assert(0 <= root and root < N);
Vec<T> ss(N, 1);
Fix([&](auto dfs, int u, int p) -> void {
for ([[maybe_unused]] const auto& [_temp_name_0, v, c] : m_edges[u]) {
if (v == p) { continue; }
dfs(v, u);
ss[u] += ss[v];
}
})(root, -1);
return ss;
}
Vec<T> depths(int root = 0) const
{
const int N = v();
assert(0 <= root and root < N);
Vec<T> ds(N, 0);
Fix([&](auto dfs, int u, int p) -> void {
for ([[maybe_unused]] const auto& [_temp_name_1, v, c] : m_edges[u]) {
if (v == p) { continue; }
ds[v] = ds[u] + c;
dfs(v, u);
}
})(root, -1);
return ds;
}
Vec<int> parents(int root = 0) const
{
const int N = v();
assert(0 <= root and root < N);
Vec<int> ps(N, -1);
Fix([&](auto dfs, int u, int p) -> void {
for ([[maybe_unused]] const auto& [_temp_name_2, v, c] : m_edges[u]) {
if (v == p) { continue; }
ps[v] = u;
dfs(v, u);
}
})(root, -1);
return ps;
}
private:
int m_v;
int m_e = 0;
Vec<Vec<Edge>> m_edges;
};
using namespace std;
struct UnionFind
{
vector<int> data;
UnionFind() = default;
explicit UnionFind(size_t sz) : data(sz, -1) {}
bool unite(int x, int y)
{
x = find(x), y = find(y);
if (x == y)
return false;
if (data[x] > data[y])
swap(x, y);
data[x] += data[y];
data[y] = x;
return true;
}
int find(int k)
{
if (data[k] < 0)
return (k);
return data[k] = find(data[k]);
}
int size(int k)
{
return -data[find(k)];
}
bool same(int x, int y)
{
return find(x) == find(y);
}
vector<vector<int>> groups()
{
int n = (int)data.size();
vector<vector<int>> ret(n);
for (int i = 0; i < n; i++) {
ret[find(i)].emplace_back(i);
}
ret.erase(remove_if(begin(ret),
end(ret),
[&](const vector<int>& v) { return v.empty(); }),
end(ret));
return ret;
}
};
/**
* @brief Bipartite Flow(二部グラフのフロー)
* @docs docs/bipartite-flow.md
*/
struct BipartiteFlow
{
size_t n, m, time_stamp;
vector<vector<int>> g, rg;
vector<int> match_l, match_r, dist, used, alive;
bool matched;
public:
explicit BipartiteFlow(size_t n, size_t m)
: n(n),
m(m),
time_stamp(0),
g(n),
rg(m),
match_l(n, -1),
match_r(m, -1),
used(n),
alive(n, 1),
matched(false)
{}
void add_edge(int u, int v)
{
g[u].push_back(v);
rg[v].emplace_back(u);
}
vector<pair<int, int>> max_matching()
{
matched = true;
for (;;) {
build_augment_path();
++time_stamp;
int flow = 0;
for (int i = 0; i < (int)n; i++) {
if (match_l[i] == -1)
flow += find_min_dist_augment_path(i);
}
if (flow == 0)
break;
}
vector<pair<int, int>> ret;
for (int i = 0; i < (int)n; i++) {
if (match_l[i] >= 0)
ret.emplace_back(i, match_l[i]);
}
return ret;
}
/* http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3198 */
void erase_edge(int a, int b)
{
if (match_l[a] == b) {
match_l[a] = -1;
match_r[b] = -1;
}
g[a].erase(find(begin(g[a]), end(g[a]), b));
rg[b].erase(find(begin(rg[b]), end(rg[b]), a));
}
/* http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0334 */
vector<pair<int, int>> lex_max_matching()
{
if (!matched)
max_matching();
for (auto& vs : g)
sort(begin(vs), end(vs));
vector<pair<int, int>> es;
for (int i = 0; i < (int)n; i++) {
if (match_l[i] == -1 || alive[i] == 0) {
continue;
}
match_r[match_l[i]] = -1;
match_l[i] = -1;
++time_stamp;
find_augment_path(i);
alive[i] = 0;
es.emplace_back(i, match_l[i]);
}
return es;
}
vector<int> min_vertex_cover()
{
auto visited = find_residual_path();
vector<int> ret;
for (int i = 0; i < (int)(n + m); i++) {
if (visited[i] ^ (i < (int)n)) {
ret.emplace_back(i);
}
}
return ret;
}
/* https://atcoder.jp/contests/utpc2013/tasks/utpc2013_11 */
vector<int> lex_min_vertex_cover(const vector<int>& ord)
{
assert(ord.size() == n + m);
auto res = build_risidual_graph();
vector<vector<int>> r_res(n + m + 2);
for (int i = 0; i < (int)(n + m + 2); i++) {
for (auto& j : res[i])
r_res[j].emplace_back(i);
}
queue<int> que;
vector<int> visited(n + m + 2, -1);
auto expand_left = [&](int t) {
if (visited[t] != -1)
return;
que.emplace(t);
visited[t] = 1;
while (!que.empty()) {
int idx = que.front();
que.pop();
for (auto& to : r_res[idx]) {
if (visited[to] != -1)
continue;
visited[to] = 1;
que.emplace(to);
}
}
};
auto expand_right = [&](int t) {
if (visited[t] != -1)
return;
que.emplace(t);
visited[t] = 0;
while (!que.empty()) {
int idx = que.front();
que.pop();
for (auto& to : res[idx]) {
if (visited[to] != -1)
continue;
visited[to] = 0;
que.emplace(to);
}
}
};
expand_right(n + m);
expand_left(n + m + 1);
vector<int> ret;
for (auto& t : ord) {
if (t < (int)n) {
expand_left(t);
if (visited[t] & 1)
ret.emplace_back(t);
} else {
expand_right(t);
if (~visited[t] & 1)
ret.emplace_back(t);
}
}
return ret;
}
vector<int> max_independent_set()
{
auto visited = find_residual_path();
vector<int> ret;
for (int i = 0; i < (int)(n + m); i++) {
if (visited[i] ^ (i >= (int)n)) {
ret.emplace_back(i);
}
}
return ret;
}
vector<pair<int, int>> min_edge_cover()
{
auto es = max_matching();
for (int i = 0; i < (int)n; i++) {
if (match_l[i] >= 0) {
continue;
}
if (g[i].empty()) {
return {};
}
es.emplace_back(i, g[i][0]);
}
for (int i = 0; i < (int)m; i++) {
if (match_r[i] >= 0) {
continue;
}
if (rg[i].empty()) {
return {};
}
es.emplace_back(rg[i][0], i);
}
return es;
}
// left: [0,n), right: [n,n+m), S: n+m, T: n+m+1
vector<vector<int>> build_risidual_graph()
{
if (!matched)
max_matching();
const size_t S = n + m;
const size_t T = n + m + 1;
vector<vector<int>> ris(n + m + 2);
for (int i = 0; i < (int)n; i++) {
if (match_l[i] == -1)
ris[S].emplace_back(i);
else
ris[i].emplace_back(S);
}
for (int i = 0; i < (int)m; i++) {
if (match_r[i] == -1)
ris[i + n].emplace_back(T);
else
ris[T].emplace_back(i + n);
}
for (int i = 0; i < (int)n; i++) {
for (auto& j : g[i]) {
if (match_l[i] == j)
ris[j + n].emplace_back(i);
else
ris[i].emplace_back(j + n);
}
}
return ris;
}
private:
vector<int> find_residual_path()
{
auto res = build_risidual_graph();
queue<int> que;
vector<int> visited(n + m + 2);
que.emplace(n + m);
visited[n + m] = true;
while (!que.empty()) {
int idx = que.front();
que.pop();
for (auto& to : res[idx]) {
if (visited[to])
continue;
visited[to] = true;
que.emplace(to);
}
}
return visited;
}
void build_augment_path()
{
queue<int> que;
dist.assign(g.size(), -1);
for (int i = 0; i < (int)n; i++) {
if (match_l[i] == -1) {
que.emplace(i);
dist[i] = 0;
}
}
while (!que.empty()) {
int a = que.front();
que.pop();
for (auto& b : g[a]) {
int c = match_r[b];
if (c >= 0 && dist[c] == -1) {
dist[c] = dist[a] + 1;
que.emplace(c);
}
}
}
}
bool find_min_dist_augment_path(int a)
{
used[a] = time_stamp;
for (auto& b : g[a]) {
int c = match_r[b];
if (c < 0
|| (used[c] != (int)time_stamp && dist[c] == dist[a] + 1
&& find_min_dist_augment_path(c))) {
match_r[b] = a;
match_l[a] = b;
return true;
}
}
return false;
}
bool find_augment_path(int a)
{
used[a] = time_stamp;
for (auto& b : g[a]) {
int c = match_r[b];
if (c < 0
|| (alive[c] == 1 && used[c] != (int)time_stamp
&& find_augment_path(c))) {
match_r[b] = a;
match_l[a] = b;
return true;
}
}
return false;
}
};
/**
* @brief Eulerian Trail(オイラー路)
* @docs docs/eulerian-trail.md
*/
template<bool directed>
struct EulerianTrail
{
vector<vector<pair<int, int>>> g;
vector<pair<int, int>> es;
int M;
vector<int> used_vertex, used_edge, deg;
explicit EulerianTrail(int V) : g(V), M(0), used_vertex(V), deg(V) {}
void add_edge(int a, int b)
{
es.emplace_back(a, b);
g[a].emplace_back(b, M);
if (directed) {
deg[a]++;
deg[b]--;
} else {
g[b].emplace_back(a, M);
deg[a]++;
deg[b]++;
}
M++;
}
pair<int, int> get_edge(int idx) const
{
return es[idx];
}
vector<vector<int>> enumerate_eulerian_trail()
{
if (directed) {
for (auto& p : deg)
if (p != 0)
return {};
} else {
for (auto& p : deg)
if (p & 1)
return {};
}
used_edge.assign(M, 0);
vector<vector<int>> ret;
for (int i = 0; i < (int)g.size(); i++) {
if (g[i].empty() || used_vertex[i])
continue;
ret.emplace_back(go(i));
}
return ret;
}
vector<vector<int>> enumerate_semi_eulerian_trail()
{
UnionFind uf(g.size());
for (auto& p : es)
uf.unite(p.first, p.second);
vector<vector<int>> group(g.size());
for (int i = 0; i < (int)g.size(); i++)
group[uf.find(i)].emplace_back(i);
vector<vector<int>> ret;
used_edge.assign(M, 0);
for (auto& vs : group) {
if (vs.empty())
continue;
int latte = -1, malta = -1;
if (directed) {
for (auto& p : vs) {
if (abs(deg[p]) > 1) {
return {};
} else if (deg[p] == 1) {
if (latte >= 0)
return {};
latte = p;
}
}
} else {
for (auto& p : vs) {
if (deg[p] & 1) {
if (latte == -1)
latte = p;
else if (malta == -1)
malta = p;
else
return {};
}
}
}
ret.emplace_back(go(latte == -1 ? vs.front() : latte));
if (ret.back().empty())
ret.pop_back();
}
return ret;
}
vector<int> go(int s)
{
stack<pair<int, int>> st;
vector<int> ord;
st.emplace(s, -1);
while (!st.empty()) {
int idx = st.top().first;
used_vertex[idx] = true;
if (g[idx].empty()) {
ord.emplace_back(st.top().second);
st.pop();
} else {
auto e = g[idx].back();
g[idx].pop_back();
if (used_edge[e.second])
continue;
used_edge[e.second] = true;
st.emplace(e);
}
}
ord.pop_back();
reverse(ord.begin(), ord.end());
return ord;
}
};
/**
* @brief Bipartite Graph Edge Coloring(二部グラフの辺彩色)
* @docs docs/bipartite-graph-edge-coloring.md
* @see https://ei1333.hateblo.jp/entry/2020/08/25/015955
*/
struct BipariteGraphEdgeColoring
{
private:
vector<vector<int>> ans;
vector<int> A, B;
int L, R;
struct RegularGraph
{
int k{}, n{};
vector<int> A, B;
};
RegularGraph g;
static UnionFind contract(valarray<int>& deg, int k)
{
using pi = pair<int, int>;
priority_queue<pi, vector<pi>, greater<>> que;
for (int i = 0; i < (int)deg.size(); i++) {
que.emplace(deg[i], i);
}
UnionFind uf(deg.size());
while (que.size() > 1) {
auto p = que.top();
que.pop();
auto q = que.top();
que.pop();
if (p.first + q.first > k)
continue;
p.first += q.first;
uf.unite(p.second, q.second);
que.emplace(p);
}
return uf;
}
RegularGraph build_k_regular_graph()
{
valarray<int> deg[2];
deg[0] = valarray<int>(L);
deg[1] = valarray<int>(R);
for (auto& p : A)
deg[0][p]++;
for (auto& p : B)
deg[1][p]++;
int k = max(deg[0].max(), deg[1].max());
/* step 1 */
UnionFind uf[2];
uf[0] = contract(deg[0], k);
uf[1] = contract(deg[1], k);
vector<int> id[2];
int ptr[] = {0, 0};
id[0] = vector<int>(L);
id[1] = vector<int>(R);
for (int i = 0; i < L; i++)
if (uf[0].find(i) == i)
id[0][i] = ptr[0]++;
for (int i = 0; i < R; i++)
if (uf[1].find(i) == i)
id[1][i] = ptr[1]++;
/* step 2 */
int N = max(ptr[0], ptr[1]);
deg[0] = valarray<int>(N);
deg[1] = valarray<int>(N);
/* step 3 */
vector<int> C, D;
C.reserve(N * k);
D.reserve(N * k);
for (int i = 0; i < (int)A.size(); i++) {
int u = id[0][uf[0].find(A[i])];
int v = id[1][uf[1].find(B[i])];
C.emplace_back(u);
D.emplace_back(v);
deg[0][u]++;
deg[1][v]++;
}
int j = 0;
for (int i = 0; i < N; i++) {
while (deg[0][i] < k) {
while (deg[1][j] == k)
++j;
C.emplace_back(i);
D.emplace_back(j);
++deg[0][i];
++deg[1][j];
}
}
return {k, N, C, D};
}
void rec(const vector<int>& ord, int k)
{
if (k == 0) {
return;
} else if (k == 1) {
ans.emplace_back(ord);
return;
} else if ((k & 1) == 0) {
EulerianTrail<false> et(g.n + g.n);
for (auto& p : ord)
et.add_edge(g.A[p], g.B[p] + g.n);
auto paths = et.enumerate_eulerian_trail();
vector<int> path;
for (auto& ps : paths) {
for (auto& e : ps)
path.emplace_back(ord[e]);
}
vector<int> beet[2];
for (int i = 0; i < (int)path.size(); i++) {
beet[i & 1].emplace_back(path[i]);
}
rec(beet[0], k / 2);
rec(beet[1], k / 2);
} else {
BipartiteFlow flow(g.n, g.n);
for (auto& i : ord)
flow.add_edge(g.A[i], g.B[i]);
flow.max_matching();
vector<int> beet;
ans.emplace_back();
for (auto& i : ord) {
if (flow.match_l[g.A[i]] == g.B[i]) {
flow.match_l[g.A[i]] = -1;
ans.back().emplace_back(i);
} else {
beet.emplace_back(i);
}
}
rec(beet, k - 1);
}
}
public:
explicit BipariteGraphEdgeColoring() : L(0), R(0) {}
void add_edge(int a, int b)
{
A.emplace_back(a);
B.emplace_back(b);
L = max(L, a + 1);
R = max(R, b + 1);
}
vector<vector<int>> build()
{
g = build_k_regular_graph();
vector<int> ord(g.A.size());
iota(ord.begin(), ord.end(), 0);
rec(ord, g.k);
vector<vector<int>> res;
for (int i = 0; i < (int)ans.size(); i++) {
res.emplace_back();
for (auto& j : ans[i])
if (j < (int)A.size())
res.back().emplace_back(j);
}
return res;
}
};
int main()
{
const auto [N, M] = in.tup<int, int>();
const auto Ass = in.vvec<int>(N, N);
Vec<int> lds(N,0), rds(N, 0);
Vec<Pair<int, int>> es;
for (int i : rep(N)) {
for (int j : rep(N)) {
lds[i] += Ass[i][j];
rds[j] += Ass[i][j];
}
}
for (int i : rep(N)) {
if (lds[i] != M) {
return out.ln(-1);
}
if (rds[i] != M) {
return out.ln(-1);
}
}
BipariteGraphEdgeColoring g;
for (int i : rep(N)) {
for (int j : rep(N)) {
for (auto _temp_name_3 [[maybe_unused]] : rep(Ass[i][j])) {
g.add_edge(i, j);
es.push_back({i, j});
}
}
}
const auto vss = g.build();
for (const auto& vs : vss) {
Vec<int> Ps(N, -1);
for (int ei : vs) {
const auto [i, j] = es[ei];
Ps[i] = j;
}
plusAll(Ps, 1);
out.ln(Ps);
}
return 0;
}