結果
| 問題 | No.2405 Minimal Matrix Decomposition |
| ユーザー |
 maspy
|
| 提出日時 | 2023-08-04 22:26:48 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 603 ms / 2,000 ms |
| コード長 | 31,645 bytes |
| コンパイル時間 | 5,367 ms |
| コンパイル使用メモリ | 317,996 KB |
| 実行使用メモリ | 9,600 KB |
| 最終ジャッジ日時 | 2024-10-14 20:26:50 |
| 合計ジャッジ時間 | 12,073 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（要ログイン）
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 | 110 ms
8,320 KB |
| testcase_05 | AC | 603 ms
9,600 KB |
| testcase_06 | AC | 2 ms
5,248 KB |
| testcase_07 | AC | 3 ms
5,248 KB |
| testcase_08 | AC | 2 ms
5,248 KB |
| testcase_09 | AC | 2 ms
5,248 KB |
| testcase_10 | AC | 203 ms
6,784 KB |
| testcase_11 | AC | 262 ms
7,552 KB |
| testcase_12 | AC | 5 ms
5,248 KB |
| testcase_13 | AC | 41 ms
5,248 KB |
| testcase_14 | AC | 53 ms
5,248 KB |
| testcase_15 | AC | 30 ms
5,248 KB |
| testcase_16 | AC | 14 ms
5,248 KB |
| testcase_17 | AC | 83 ms
5,504 KB |
| testcase_18 | AC | 87 ms
5,376 KB |
| testcase_19 | AC | 101 ms
5,500 KB |
| testcase_20 | AC | 7 ms
5,248 KB |
| testcase_21 | AC | 16 ms
5,248 KB |
| testcase_22 | AC | 189 ms
6,912 KB |
| testcase_23 | AC | 3 ms
5,248 KB |
| testcase_24 | AC | 5 ms
5,248 KB |
| testcase_25 | AC | 15 ms
5,248 KB |
| testcase_26 | AC | 153 ms
6,016 KB |
| testcase_27 | AC | 32 ms
5,248 KB |
| testcase_28 | AC | 188 ms
6,272 KB |
| testcase_29 | AC | 57 ms
5,248 KB |
| testcase_30 | AC | 166 ms
6,400 KB |
| testcase_31 | AC | 53 ms
5,248 KB |
| testcase_32 | AC | 13 ms
5,248 KB |
| testcase_33 | AC | 142 ms
5,888 KB |
| testcase_34 | AC | 20 ms
5,248 KB |
| testcase_35 | AC | 2 ms
5,248 KB |
| testcase_36 | AC | 47 ms
5,248 KB |
| testcase_37 | AC | 59 ms
5,376 KB |
| testcase_38 | AC | 114 ms
5,748 KB |
| testcase_39 | AC | 188 ms
6,516 KB |
| testcase_40 | AC | 66 ms
5,760 KB |
| testcase_41 | AC | 7 ms
5,248 KB |
| testcase_42 | AC | 157 ms
6,664 KB |
| testcase_43 | AC | 34 ms
5,248 KB |
| testcase_44 | AC | 29 ms
5,248 KB |
| testcase_45 | AC | 11 ms
5,248 KB |
| testcase_46 | AC | 33 ms
5,248 KB |
| testcase_47 | AC | 38 ms
5,248 KB |
| testcase_48 | AC | 12 ms
5,248 KB |
| testcase_49 | AC | 5 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 3 "main.cpp"
#line 2 "/home/maspy/compro/library/mod/modint_common.hpp"
struct has_mod_impl {
template <class T>
static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};
template <typename mint>
mint inv(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {0, 1};
assert(0 <= n);
if (n >= mod) n %= mod;
while (len(dat) <= n) {
int k = len(dat);
int q = (mod + k - 1) / k;
dat.eb(dat[k * q - mod] * mint(q));
}
return dat[n];
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
assert(0 <= n);
if (n >= mod) return 0;
static vector<mint> dat = {1, 1};
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint(len(dat)));
return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
static vector<mint> dat = {1, 1};
if (n < 0) return mint(0);
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
return dat[n];
}
template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
return (mint(1) * ... * fact_inv<mint>(xs));
}
template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}
template <typename mint>
mint C_dense(int n, int k) {
static vvc<mint> C;
static int H = 0, W = 0;
auto calc = [&](int i, int j) -> mint {
if (i == 0) return (j == 0 ? mint(1) : mint(0));
return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
};
if (W <= k) {
FOR(i, H) {
C[i].resize(k + 1);
FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
}
W = k + 1;
}
if (H <= n) {
C.resize(n + 1);
FOR(i, H, n + 1) {
C[i].resize(W);
FOR(j, W) { C[i][j] = calc(i, j); }
}
H = n + 1;
}
return C[n][k];
}
template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
if (dense) return C_dense<mint>(n, k);
if (!large) return multinomial<mint>(n, k, n - k);
k = min(k, n - k);
mint x(1);
FOR(i, k) x *= mint(n - i);
return x * fact_inv<mint>(k);
}
template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
assert(n >= 0);
assert(0 <= k && k <= n);
if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
return mint(1) / C<mint, 1>(n, k);
}
// [x^d] (1-x) ^ {-n} の計算
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
assert(n >= 0);
if (d < 0) return mint(0);
if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
return C<mint, large, dense>(n + d - 1, d);
}
#line 2 "/home/maspy/compro/library/mod/primitive_root.hpp"
#line 2 "/home/maspy/compro/library/nt/primetest.hpp"
struct m64 {
using i64 = int64_t;
using u64 = uint64_t;
using u128 = __uint128_t;
inline static u64 m, r, n2; // r * m = -1 (mod 1<<64), n2 = 1<<128 (mod m)
static void set_mod(u64 m) {
assert((m & 1) == 1);
m64::m = m;
n2 = -u128(m) % m;
r = m;
FOR(_, 5) r *= 2 - m * r;
r = -r;
assert(r * m == -1ull);
}
static u64 reduce(u128 b) { return (b + u128(u64(b) * r) * m) >> 64; }
u64 x;
m64() : x(0) {}
m64(u64 x) : x(reduce(u128(x) * n2)){};
u64 val() const {
u64 y = reduce(x);
return y >= m ? y - m : y;
}
m64 &operator+=(m64 y) {
x += y.x - (m << 1);
x = (i64(x) < 0 ? x + (m << 1) : x);
return *this;
}
m64 &operator-=(m64 y) {
x -= y.x;
x = (i64(x) < 0 ? x + (m << 1) : x);
return *this;
}
m64 &operator*=(m64 y) {
x = reduce(u128(x) * y.x);
return *this;
}
m64 operator+(m64 y) const { return m64(*this) += y; }
m64 operator-(m64 y) const { return m64(*this) -= y; }
m64 operator*(m64 y) const { return m64(*this) *= y; }
bool operator==(m64 y) const {
return (x >= m ? x - m : x) == (y.x >= m ? y.x - m : y.x);
}
bool operator!=(m64 y) const { return not operator==(y); }
m64 pow(u64 n) const {
m64 y = 1, z = *this;
for (; n; n >>= 1, z *= z)
if (n & 1) y *= z;
return y;
}
};
bool primetest(const uint64_t x) {
using u64 = uint64_t;
if (x == 2 or x == 3 or x == 5 or x == 7) return true;
if (x % 2 == 0 or x % 3 == 0 or x % 5 == 0 or x % 7 == 0) return false;
if (x < 121) return x > 1;
const u64 d = (x - 1) >> __builtin_ctzll(x - 1);
m64::set_mod(x);
const m64 one(1), minus_one(x - 1);
auto ok = [&](u64 a) {
auto y = m64(a).pow(d);
u64 t = d;
while (y != one and y != minus_one and t != x - 1) y *= y, t <<= 1;
if (y != minus_one and t % 2 == 0) return false;
return true;
};
if (x < (1ull << 32)) {
for (u64 a: {2, 7, 61})
if (not ok(a)) return false;
} else {
for (u64 a: {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
if (x <= a) return true;
if (not ok(a)) return false;
}
}
return true;
}
#line 3 "/home/maspy/compro/library/nt/factor.hpp"
mt19937_64 rng_mt{random_device{}()};
ll rnd(ll n) { return uniform_int_distribution<ll>(0, n - 1)(rng_mt); }
ll rho(ll n, ll c) {
m64::set_mod(n);
assert(n > 1);
const m64 cc(c);
auto f = [&](m64 x) { return x * x + cc; };
m64 x = 1, y = 2, z = 1, q = 1;
ll g = 1;
const ll m = 1LL << (__lg(n) / 5); // ?
for (ll r = 1; g == 1; r <<= 1) {
x = y;
FOR(_, r) y = f(y);
for (ll k = 0; k < r and g == 1; k += m) {
z = y;
FOR(_, min(m, r - k)) y = f(y), q *= x - y;
g = gcd(q.val(), n);
}
}
if (g == n) do {
z = f(z);
g = gcd((x - z).val(), n);
} while (g == 1);
return g;
}
ll find_prime_factor(ll n) {
assert(n > 1);
if (primetest(n)) return n;
FOR(_, 100) {
ll m = rho(n, rnd(n));
if (primetest(m)) return m;
n = m;
}
cerr << "failed" << endl;
assert(false);
return -1;
}
// ソートしてくれる
vc<pair<ll, int>> factor(ll n) {
assert(n >= 1);
vc<pair<ll, int>> pf;
FOR3(p, 2, 100) {
if (p * p > n) break;
if (n % p == 0) {
ll e = 0;
do { n /= p, e += 1; } while (n % p == 0);
pf.eb(p, e);
}
}
while (n > 1) {
ll p = find_prime_factor(n);
ll e = 0;
do { n /= p, e += 1; } while (n % p == 0);
pf.eb(p, e);
}
sort(all(pf));
return pf;
}
vc<pair<ll, int>> factor_by_lpf(ll n, vc<int>& lpf) {
vc<pair<ll, int>> res;
while (n > 1) {
int p = lpf[n];
int e = 0;
while (n % p == 0) {
n /= p;
++e;
}
res.eb(p, e);
}
return res;
}
#line 2 "/home/maspy/compro/library/mod/barrett.hpp"
// https://github.com/atcoder/ac-library/blob/master/atcoder/internal_math.hpp
struct Barrett {
u32 m;
u64 im;
explicit Barrett(u32 m = 1) : m(m), im(u64(-1) / m + 1) {}
u32 umod() const { return m; }
u32 modulo(u64 z) {
if (m == 1) return 0;
u64 x = (u64)(((unsigned __int128)(z)*im) >> 64);
u64 y = x * m;
return (z - y + (z < y ? m : 0));
}
u64 floor(u64 z) {
if (m == 1) return z;
u64 x = (u64)(((unsigned __int128)(z)*im) >> 64);
u64 y = x * m;
return (z < y ? x - 1 : x);
}
pair<u64, u32> divmod(u64 z) {
if (m == 1) return {z, 0};
u64 x = (u64)(((unsigned __int128)(z)*im) >> 64);
u64 y = x * m;
if (z < y) return {x - 1, z - y + m};
return {x, z - y};
}
u32 mul(u32 a, u32 b) { return modulo(u64(a) * b); }
};
#line 3 "/home/maspy/compro/library/mod/mod_pow.hpp"
// int
ll mod_pow(ll a, ll n, int mod) {
assert(n >= 0);
a %= mod;
if (a < 0) a += mod;
Barrett bt(mod);
ll p = a, v = bt.modulo(1);
while (n) {
if (n & 1) v = bt.mul(v, p);
p = bt.mul(p, p);
n >>= 1;
}
return v;
}
ll mod_pow_long(ll a, ll n, ll mod) {
assert(n >= 0);
a %= mod;
if (a < 0) a += mod;
ll p = a, v = 1 % mod;
while (n) {
if (n & 1) v = i128(v) * p % mod;
p = i128(p) * p % mod;
n >>= 1;
}
return v;
}
#line 2 "/home/maspy/compro/library/random/base.hpp"
u64 RNG_64() {
static uint64_t x_
= uint64_t(chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count())
* 10150724397891781847ULL;
x_ ^= x_ << 7;
return x_ ^= x_ >> 9;
}
u64 RNG(u64 lim) { return RNG_64() % lim; }
ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 6 "/home/maspy/compro/library/mod/primitive_root.hpp"
// int
int primitive_root(int p) {
auto pf = factor(p - 1);
auto is_ok = [&](int g) -> bool {
for (auto&& [q, e]: pf)
if (mod_pow(g, (p - 1) / q, p) == 1) return false;
return true;
};
while (1) {
int x = RNG(1, p);
if (is_ok(x)) return x;
}
return -1;
}
ll primitive_root_long(ll p) {
auto pf = factor(p - 1);
auto is_ok = [&](ll g) -> bool {
for (auto&& [q, e]: pf)
if (mod_pow_long(g, (p - 1) / q, p) == 1) return false;
return true;
};
while (1) {
ll x = RNG(1, p);
if (is_ok(x)) return x;
}
return -1;
}
#line 5 "/home/maspy/compro/library/mod/dynamic_modint.hpp"
template <class T>
using is_signed_int =
typename std::conditional<(is_integral<T>::value
&& std::is_signed<T>::value),
std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value
&& std::is_unsigned<T>::value),
std::true_type, std::false_type>::type;
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
struct Dynamic_Modint {
static constexpr bool is_modint = true;
using mint = Dynamic_Modint;
u32 val;
static Barrett bt;
static u32 umod() { return bt.umod(); }
static int get_mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = Barrett(m);
}
Dynamic_Modint() : val(0) {}
template <class T, is_signed_int_t<T>* = nullptr>
Dynamic_Modint(T v) {
int x = v % get_mod();
if (x < 0) x += get_mod();
val = u32(x);
}
template <class T, is_unsigned_int_t<T>* = nullptr>
Dynamic_Modint(T v) {
val = bt.modulo(v);
}
mint& operator+=(const mint& rhs) {
val += rhs.val;
if (val >= umod()) val -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
val += umod() - rhs.val;
if (val >= umod()) val -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
val = bt.mul(val, rhs.val);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inverse(); }
mint operator-() const { return mint() - *this; }
mint pow(ll n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inverse() const {
int x = val;
int mod = get_mod();
ll a = x, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
if (u < 0) u += mod;
return u;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs.val != rhs.val;
}
#ifdef FASTIO
void write() { fastio::printer.write(val); }
void read() {
fastio::scanner.read(val);
assert(0 <= val && val < u32(get_mod()));
}
#endif
static pair<int, int>& get_ntt() {
static pair<int, int> p = {-1, -1};
return p;
}
static void set_ntt_info() {
int mod = get_mod();
int k = lowbit(mod - 1);
int r = primitive_root(mod);
r = mod_pow(r, (mod - 1) >> k, mod);
get_ntt() = {k, r};
}
static pair<int, int> ntt_info() { return get_ntt(); }
static bool can_ntt() { return ntt_info().fi != -1; }
};
using dmint = Dynamic_Modint;
Barrett dmint::bt(1);
#line 3 "/home/maspy/compro/library/mod/modint.hpp"
template <int mod>
struct modint {
static_assert(mod < (1 << 30));
int val;
constexpr modint(const ll val = 0) noexcept
: val(val >= 0 ? val % mod : (mod - (-val) % mod) % mod) {}
bool operator<(const modint &other) const {
return val < other.val;
} // To use std::map
modint &operator+=(const modint &p) {
if ((val += p.val) >= mod) val -= mod;
return *this;
}
modint &operator-=(const modint &p) {
if ((val += mod - p.val) >= mod) val -= mod;
return *this;
}
modint &operator*=(const modint &p) {
val = (int)(1LL * val * p.val % mod);
return *this;
}
modint &operator/=(const modint &p) {
*this *= p.inverse();
return *this;
}
modint operator-() const { return modint(-val); }
modint operator+(const modint &p) const { return modint(*this) += p; }
modint operator-(const modint &p) const { return modint(*this) -= p; }
modint operator*(const modint &p) const { return modint(*this) *= p; }
modint operator/(const modint &p) const { return modint(*this) /= p; }
bool operator==(const modint &p) const { return val == p.val; }
bool operator!=(const modint &p) const { return val != p.val; }
modint inverse() const {
int a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return modint(u);
}
modint pow(ll n) const {
assert(n >= 0);
modint ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
#ifdef FASTIO
void write() { fastio::printer.write(val); }
void read() {
fastio::scanner.read(val);
val = (val >= 0 ? val % mod : (mod - (-val) % mod) % mod);
}
#endif
static constexpr int get_mod() { return mod; }
// (n, r), r は 1 の 2^n 乗根
static constexpr pair<int, int> ntt_info() {
if (mod == 167772161) return {25, 17};
if (mod == 469762049) return {26, 30};
if (mod == 754974721) return {24, 362};
if (mod == 880803841) return {23, 211};
if (mod == 998244353) return {23, 31};
if (mod == 1045430273) return {20, 363};
if (mod == 1051721729) return {20, 330};
if (mod == 1053818881) return {20, 2789};
return {-1, -1};
}
static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 3 "/home/maspy/compro/library/linalg/mat_mul.hpp"
template <class T, typename enable_if<has_mod<T>::value>::type* = nullptr>
vc<vc<T>> mat_mul(const vc<vc<T>>& A, const vc<vc<T>>& B) {
const int mod = T::get_mod();
auto N = len(A), M = len(B), K = len(B[0]);
vv(int, b, K, M);
FOR(i, M) FOR(j, K) b[j][i] = B[i][j].val;
vv(T, C, N, K);
if (M <= 16) {
FOR(i, N) FOR(j, K) {
u64 sm = 0;
FOR(m, M) sm += u64(A[i][m].val) * b[j][m];
C[i][j] = sm % mod;
}
} else {
FOR(i, N) FOR(j, K) {
i128 sm = 0;
FOR(m, M) sm += ll(A[i][m].val) * b[j][m];
C[i][j] = int(sm % mod);
}
}
return C;
}
template <class T, typename enable_if<!has_mod<T>::value>::type* = nullptr>
vc<vc<T>> mat_mul(const vc<vc<T>>& A, const vc<vc<T>>& B) {
assert(!A.empty() && !B.empty());
auto N = len(A), M = len(B), K = len(B[0]);
vv(T, b, K, M);
FOR(i, M) FOR(j, K) b[j][i] = B[i][j];
vv(T, C, N, K);
FOR(n, N) FOR(m, M) FOR(k, K) C[n][k] += A[n][m] * b[k][m];
return C;
}
#line 6 "main.cpp"
/*
template <typename T>
int matrix_rank(const int n, const int m, vc<vc<T>> a) {
int rk = 0;
FOR(j, m) {
if (rk == n) break;
if (a[rk][j] == 0) {
FOR3(i, rk + 1, n) if (a[i][j] != 0) {
swap(a[rk], a[i]);
break;
}
}
if (a[rk][j] == 0) continue;
T c = T(1) / a[rk][j];
FOR(k, j, m) a[rk][k] *= c;
FOR(i, rk + 1, n) {
T c = a[i][j];
FOR3(k, j, m) { a[i][k] -= a[rk][k] * c; }
}
++rk;
}
return rk;
}
*/
using mint = dmint;
pair<vvc<mint>, vvc<mint>> F(vvc<mint> a) {
vvc<mint> a0 = a;
ll n = len(a), m = len(a[0]);
int rk = 0;
vv(mint, P, n, n);
vv(mint, Q, m, m);
FOR(i, n) P[i][i] = 1;
FOR(j, m) Q[j][j] = 1;
vc<int> pivot_col;
FOR(j, m) {
if (rk == n) break;
if (a[rk][j] == 0) {
FOR(i, rk + 1, n) if (a[i][j] != 0) {
swap(a[rk], a[i]);
FOR(k, n) swap(P[k][i], P[k][rk]);
break;
}
}
if (a[rk][j] == 0) continue;
pivot_col.eb(j);
mint c = mint(1) / a[rk][j];
FOR(i, n) P[i][rk] *= a[rk][j];
FOR(k, j, m) a[rk][k] *= c;
FOR(i, n) {
if (i == rk) continue;
mint c = a[i][j];
FOR3(k, j, m) { a[i][k] -= a[rk][k] * c; }
FOR(k, n) { P[k][rk] += c * P[k][i]; }
}
++rk;
}
FOR(k, rk) {
int p = pivot_col[k];
if (p == k) continue;
FOR(i, n) { swap(a[i][p], a[i][k]); }
swap(Q[p], Q[k]);
}
FOR(i, rk) {
FOR(j, i + 1, m) {
mint c = a[i][j];
a[i][j] -= c;
FOR(k, m) Q[i][k] += c * Q[j][k];
}
}
FOR(i, n) FOR(j, m) {
if (i == j && i < rk) {
assert(a[i][j] == mint(1));
} else {
assert(a[i][j] == mint(0));
}
}
vvc<mint> b = mat_mul(mat_mul(P, a), Q);
assert(a0 == b);
int w = max(rk, 1);
vv(mint, L, n, w);
vv(mint, R, w, m);
FOR(i, rk) L[i][i] = R[i][i] = mint(1);
L = mat_mul(P, L);
R = mat_mul(R, Q);
b = mat_mul(L, R);
assert(a0 == b);
return {L, R};
}
void solve() {
LL(mod);
mint::set_mod(mod);
LL(N, M);
vv(mint, A, N, M);
FOR(i, N) FOR(j, M) read(A[i][j]);
auto [X, Y] = F(A);
ll NX = len(X), MX = len(X[0]);
ll NY = len(Y), MY = len(Y[0]);
if (N * M < NX * MX + NY * MY) {
print(1);
print(N, M);
FOR(i, N) print(A[i]);
} else {
print(2);
print(NX, MX);
FOR(i, NX) print(X[i]);
print(NY, MY);
FOR(i, NY) print(Y[i]);
}
}
signed main() {
int T = 1;
// INT(T);
FOR(T) solve();
return 0;
}