結果
| 問題 | No.578 3 x N グリッド上のサイクルのサイズ(easy) |
| ユーザー |
 maspy
|
| 提出日時 | 2022-10-24 21:35:43 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 4 ms / 2,000 ms |
| コード長 | 45,268 bytes |
| コンパイル時間 | 7,095 ms |
| コンパイル使用メモリ | 340,676 KB |
| 実行使用メモリ | 12,140 KB |
| 最終ジャッジ日時 | 2024-07-03 00:31:05 |
| 合計ジャッジ時間 | 8,733 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / 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
5,376 KB |
| testcase_03 | AC | 2 ms
5,376 KB |
| testcase_04 | AC | 1 ms
5,376 KB |
| testcase_05 | AC | 2 ms
5,376 KB |
| testcase_06 | AC | 2 ms
5,376 KB |
| testcase_07 | AC | 2 ms
5,376 KB |
| testcase_08 | AC | 2 ms
5,376 KB |
| testcase_09 | AC | 2 ms
5,376 KB |
| testcase_10 | AC | 3 ms
5,376 KB |
| testcase_11 | AC | 2 ms
5,376 KB |
| testcase_12 | AC | 2 ms
5,376 KB |
| testcase_13 | AC | 2 ms
5,376 KB |
| testcase_14 | AC | 2 ms
5,376 KB |
| testcase_15 | AC | 2 ms
5,376 KB |
| testcase_16 | AC | 2 ms
5,376 KB |
| testcase_17 | AC | 2 ms
5,376 KB |
| testcase_18 | AC | 2 ms
5,376 KB |
| testcase_19 | AC | 2 ms
5,376 KB |
| testcase_20 | AC | 2 ms
5,376 KB |
| testcase_21 | AC | 2 ms
5,376 KB |
| testcase_22 | AC | 2 ms
5,376 KB |
| testcase_23 | AC | 2 ms
5,376 KB |
| testcase_24 | AC | 2 ms
5,376 KB |
| testcase_25 | AC | 2 ms
5,376 KB |
| testcase_26 | AC | 2 ms
5,376 KB |
| testcase_27 | AC | 2 ms
5,376 KB |
| testcase_28 | AC | 2 ms
5,376 KB |
| testcase_29 | AC | 2 ms
5,376 KB |
| testcase_30 | AC | 2 ms
5,376 KB |
| testcase_31 | AC | 2 ms
5,376 KB |
| testcase_32 | AC | 2 ms
5,376 KB |
| testcase_33 | AC | 1 ms
5,376 KB |
| testcase_34 | AC | 2 ms
5,376 KB |
| testcase_35 | AC | 1 ms
5,376 KB |
| testcase_36 | AC | 2 ms
5,376 KB |
| testcase_37 | AC | 3 ms
12,020 KB |
| testcase_38 | AC | 4 ms
12,000 KB |
| testcase_39 | AC | 3 ms
9,968 KB |
| testcase_40 | AC | 4 ms
9,852 KB |
| testcase_41 | AC | 3 ms
12,140 KB |
| testcase_42 | AC | 3 ms
12,004 KB |
| testcase_43 | AC | 2 ms
10,092 KB |
| testcase_44 | AC | 3 ms
12,000 KB |
| testcase_45 | AC | 3 ms
12,004 KB |
| testcase_46 | AC | 3 ms
9,952 KB |
| testcase_47 | AC | 2 ms
6,940 KB |
| testcase_48 | AC | 3 ms
10,076 KB |
| testcase_49 | AC | 3 ms
12,036 KB |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
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 vec(type, name, ...) vector<type> name(__VA_ARGS__)
#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 FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) \
overload4(__VA_ARGS__, FOR4_R, 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
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())
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>
T pick(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T pick(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T pick(pqg<T> &que) {
assert(que.size());
T a = que.top();
que.pop();
return a;
}
template <typename T>
T pick(vc<T> &que) {
assert(que.size());
T a = que.back();
que.pop_back();
return a;
}
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 F>
ll binary_search(F check, ll ok, ll ng) {
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);
}
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = S[i] - first_char; }
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;
}
template <typename CNT, typename T>
vc<CNT> bincount(const vc<T> &A, int size) {
vc<CNT> C(size);
for (auto &&x: A) { ++C[x]; }
return C;
}
// stable
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(A.size());
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
int n = len(I);
vc<T> B(n);
FOR(i, n) B[i] = A[I[i]];
return B;
}
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>
namespace detail {
template <typename T, decltype(&T::is_modint) = &T::is_modint>
std::true_type check_value(int);
template <typename T>
std::false_type check_value(long);
} // namespace detail
template <typename T>
struct is_modint : decltype(detail::check_value<T>(0)) {};
template <typename T>
using is_modint_t = enable_if_t<is_modint<T>::value>;
template <typename T>
using is_not_modint_t = enable_if_t<!is_modint<T>::value>;
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 <class T, is_modint_t<T> * = nullptr>
bool read_single(T &ref) {
long long val = 0;
bool f = read_single(val);
ref = T(val);
return f;
}
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 <class A, class B, class C>
bool read_single(tuple<A, B, C> &p) {
return (read_single(get<0>(p)) && read_single(get<1>(p))
&& read_single(get<2>(p)));
}
template <class A, class B, class C, class D>
bool read_single(tuple<A, B, C, D> &p) {
return (read_single(get<0>(p)) && read_single(get<1>(p))
&& read_single(get<2>(p)) && read_single(get<3>(p)));
}
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 <class T, is_modint_t<T> * = nullptr>
void write(T &ref) {
write(ref.val);
}
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 <class A, class B, class C>
void write(const tuple<A, B, C> &val) {
auto &[a, b, c] = val;
write(a), write(' '), write(b), write(' '), write(c);
}
template <class A, class B, class C, class D>
void write(const tuple<A, B, C, D> &val) {
auto &[a, b, c, d] = val;
write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d);
}
template <class A, class B, class C, class D, class E>
void write(const tuple<A, B, C, D, E> &val) {
auto &[a, b, c, d, e] = val;
write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e);
}
template <class A, class B, class C, class D, class E, class F>
void write(const tuple<A, B, C, D, E, F> &val) {
auto &[a, b, c, d, e, f] = val;
write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f);
}
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...);
}
#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.hpp"
template <int mod>
struct modint {
static constexpr bool is_modint = true;
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(int64_t n) const {
modint ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
static constexpr int get_mod() { return mod; }
};
struct ArbitraryModInt {
static constexpr bool is_modint = true;
int val;
ArbitraryModInt() : val(0) {}
ArbitraryModInt(int64_t y)
: val(y >= 0 ? y % get_mod()
: (get_mod() - (-y) % get_mod()) % get_mod()) {}
bool operator<(const ArbitraryModInt &other) const {
return val < other.val;
} // To use std::map<ArbitraryModInt, T>
static int &get_mod() {
static int mod = 0;
return mod;
}
static void set_mod(int md) { get_mod() = md; }
ArbitraryModInt &operator+=(const ArbitraryModInt &p) {
if ((val += p.val) >= get_mod()) val -= get_mod();
return *this;
}
ArbitraryModInt &operator-=(const ArbitraryModInt &p) {
if ((val += get_mod() - p.val) >= get_mod()) val -= get_mod();
return *this;
}
ArbitraryModInt &operator*=(const ArbitraryModInt &p) {
long long a = (long long)val * p.val;
int xh = (int)(a >> 32), xl = (int)a, d, m;
asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(get_mod()));
val = m;
return *this;
}
ArbitraryModInt &operator/=(const ArbitraryModInt &p) {
*this *= p.inverse();
return *this;
}
ArbitraryModInt operator-() const { return ArbitraryModInt(get_mod() - val); }
ArbitraryModInt operator+(const ArbitraryModInt &p) const {
return ArbitraryModInt(*this) += p;
}
ArbitraryModInt operator-(const ArbitraryModInt &p) const {
return ArbitraryModInt(*this) -= p;
}
ArbitraryModInt operator*(const ArbitraryModInt &p) const {
return ArbitraryModInt(*this) *= p;
}
ArbitraryModInt operator/(const ArbitraryModInt &p) const {
return ArbitraryModInt(*this) /= p;
}
bool operator==(const ArbitraryModInt &p) const { return val == p.val; }
bool operator!=(const ArbitraryModInt &p) const { return val != p.val; }
ArbitraryModInt inverse() const {
int a = val, b = get_mod(), u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return ArbitraryModInt(u);
}
ArbitraryModInt pow(int64_t n) const {
ArbitraryModInt ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
};
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 (int(dat.size()) <= n) {
int k = dat.size();
auto q = (mod + k - 1) / k;
int r = k * q - mod;
dat.emplace_back(dat[r] * mint(q));
}
return dat[n];
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {1, 1};
assert(0 <= n);
if (n >= mod) return 0;
while (int(dat.size()) <= n) {
int k = dat.size();
dat.emplace_back(dat[k - 1] * mint(k));
}
return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {1, 1};
assert(0 <= n && n < mod);
while (int(dat.size()) <= n) {
int k = dat.size();
dat.emplace_back(dat[k - 1] * inv<mint>(k));
}
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 fact<mint>(n) * fact_inv<mint>(k) * fact_inv<mint>(n - k);
k = min(k, n - k);
mint x(1);
FOR(i, k) { x *= mint(n - i); }
x *= fact_inv<mint>(k);
return x;
}
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);
}
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
using amint = ArbitraryModInt;
#line 2 "/home/maspy/compro/library/ds/hashmap.hpp"
template <typename Val, int LOG = 20>
struct HashMapLL {
int N;
ll* keys;
Val* vals;
vc<int> IDS;
bitset<1 << LOG> used;
const int shift;
const uint64_t r = 11995408973635179863ULL;
HashMapLL()
: N(1 << LOG), keys(new ll[N]), vals(new Val[N]), shift(64 - __lg(N)) {}
int hash(ll x) {
static const uint64_t FIXED_RANDOM
= std::chrono::steady_clock::now().time_since_epoch().count();
return (uint64_t(x + FIXED_RANDOM) * r) >> shift;
}
int index(const ll& key) {
int i = 0;
for (i = hash(key); used[i] && keys[i] != key; (i += 1) &= (N - 1)) {}
return i;
}
Val& operator[](const ll& key) {
int i = index(key);
if (!used[i]) IDS.eb(i), used[i] = 1, keys[i] = key, vals[i] = Val{};
return vals[i];
}
Val get(const ll& key, Val default_value) {
int i = index(key);
if (!used[i]) return default_value;
return vals[i];
}
bool contain(const ll& key) {
int i = index(key);
return used[i] && keys[i] == key;
}
bool count(const ll& key) {
int i = index(key);
return used[i] && keys[i] == key;
}
void reset() {
for (auto&& i: IDS) used[i] = 0;
IDS.clear();
}
vc<pair<ll, Val>> items() {
vc<pair<ll, Val>> res;
res.reserve(len(IDS));
for (auto&& i: IDS) res.eb(keys[i], vals[i]);
return res;
}
};
template <typename KEY, typename VAL, int LOG>
struct HashMap {
HashMapLL<VAL, LOG> MP;
function<ll(KEY)> f;
HashMap(function<ll(KEY)> f) : MP(), f(f) {}
int index(const KEY& key) { return MP.index(f(key)); }
VAL& operator[](const KEY& key) { return MP[f(key)]; }
bool contain(const KEY& key) { return MP.contain(f(key)); }
bool count(const KEY& key) { return MP.count(f(key)); }
void reset() { MP.reset(); }
};
#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 2 "/home/maspy/compro/library/mod/modint61.hpp"
struct modint61 {
static constexpr bool is_modint = true;
static constexpr ll mod = (1LL << 61) - 1;
ll val;
constexpr modint61(const ll x = 0) : val(x) {
while(val < 0) val += mod;
while(val >= mod) val -= mod;
}
bool operator<(const modint61 &other) const {
return val < other.val;
} // To use std::map
bool operator==(const modint61 &p) const { return val == p.val; }
bool operator!=(const modint61 &p) const { return val != p.val; }
modint61 &operator+=(const modint61 &p) {
if ((val += p.val) >= mod) val -= mod;
return *this;
}
modint61 &operator-=(const modint61 &p) {
if ((val += mod - p.val) >= mod) val -= mod;
return *this;
}
modint61 &operator*=(const modint61 &p) {
ll a = val, b = p.val;
const ll MASK30 = (1LL << 30) - 1;
const ll MASK31 = (1LL << 31) - 1;
const ll MASK61 = (1LL << 61) - 1;
ll au = a >> 31, ad = a & MASK31;
ll bu = b >> 31, bd = b & MASK31;
ll x = ad * bu + au * bd;
ll xu = x >> 30, xd = x & MASK30;
x = au * bu * 2 + xu + (xd << 31) + ad * bd;
xu = x >> 61, xd = x & MASK61;
x = xu + xd;
if (x >= MASK61) x -= MASK61;
val = x;
return *this;
}
modint61 operator-() const { return modint61(get_mod() - val); }
modint61 &operator/=(const modint61 &p) {
*this *= p.inverse();
return *this;
}
modint61 operator+(const modint61 &p) const { return modint61(*this) += p; }
modint61 operator-(const modint61 &p) const { return modint61(*this) -= p; }
modint61 operator*(const modint61 &p) const { return modint61(*this) *= p; }
modint61 operator/(const modint61 &p) const { return modint61(*this) /= p; }
modint61 inverse() const {
ll 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 modint61(u);
}
modint61 pow(int64_t n) const {
modint61 ret(1), mul(val);
while (n > 0) {
if (n & 1) ret = ret * mul;
mul = mul * mul;
n >>= 1;
}
return ret;
}
static constexpr ll get_mod() { return mod; }
};
#line 3 "/home/maspy/compro/library/random/hash_vector.hpp"
template <typename T>
ll hash_vector(vc<T> X) {
using mint = modint61;
static vc<mint> hash_base;
int n = len(X);
while (len(hash_base) <= n) { hash_base.eb(RNG(mint::get_mod())); }
mint H = 0;
FOR(i, n) H += hash_base[i] * mint(X[i]);
H += hash_base[n];
return H.val;
}
#line 3 "/home/maspy/compro/library/connected_dp/squares.hpp"
namespace connected_dp_squares {
// pair<新しい状態、今の成分 → 新しい成分>
vc<pair<vc<int>, vc<int>>> next_states(const vc<int>& now) {
int N = len(now);
vc<pair<vc<int>, vc<int>>> res;
FOR(s, 1 << N) {
vc<int> par(N + N);
FOR(i, N) par[i] = (s & 1 << i ? i : -1);
FOR(i, N) par[N + i] = (now[i] == -1 ? -1 : now[i] + N);
auto find = [&](int x) -> int {
while (par[x] != x) { x = par[x] = par[par[x]]; }
return x;
};
auto merge = [&](int a, int b) -> void {
a = find(a), b = find(b);
if (a == b) return;
if (a > b) swap(a, b);
par[b] = a;
};
FOR(i, N - 1) if (par[i] != -1 && par[i + 1] != -1) merge(i, i + 1);
FOR(i, N) if (par[i] != -1 && par[N + i] != -1) merge(i, N + i);
FOR(i, N + N) if (par[i] != -1) par[i] = find(i);
FOR(i, N, N + N) if (par[i] >= N) par[i] = -1;
res.eb(vc<int>(par.begin(), par.begin() + N),
vc<int>(par.begin() + N, par.end()));
}
return res;
}
vc<int> reverse_state(const vc<int>& now) {
int N = len(now);
vc<int> max_i(N, -1);
FOR(i, N) if (now[i] != -1) max_i[now[i]] = i;
vc<int> rev(N, -1);
FOR(i, N) {
if (now[i] == -1) continue;
int x = max_i[now[i]];
rev[N - 1 - i] = N - 1 - x;
}
return rev;
}
// 0, 1 ：空の列、領域の手前、後ろ
// 連結領域をひとつ作る。多角形とは限らない。
pair<vvc<int>, vc<pair<int, int>>> connedted_dp_graph(int N,
bool merge_reverse) {
static HashMapLL<int> MP;
MP.reset();
vvc<int> states;
vc<pair<int, int>> edges;
states.eb(vc<int>(N, -1));
states.eb(vc<int>(N, -1));
MP[hash_vector<int>(states[0])] = 0;
int p = -1;
while (1) {
if (++p == len(states)) break;
if (p == 1) {
edges.eb(1, 1);
continue;
}
vc<int> now = states[p];
for (auto&& [nxt, convert]: next_states(now)) {
// 今の成分数、消える成分数
int a = 0, b = 0;
FOR(v, N) if (now[v] == v) {
++a;
if (convert[v] == -1) ++b;
}
// 消える成分があってよいのは、終状態にいくときのみ
if (b >= 2) continue;
if (b == 1) {
if (MAX(nxt) != -1) continue;
edges.eb(p, 1);
continue;
}
ll h = hash_vector<int>(nxt);
if (merge_reverse) { chmin(h, hash_vector<int>(reverse_state(nxt))); }
if (!MP.count(h)) {
MP[h] = len(states);
states.eb(nxt);
}
edges.eb(p, MP[h]);
}
}
return {states, edges};
}
pair<vvc<int>, vc<pair<int, int>>> polygon_dp_graph(int N) {
static HashMapLL<int> MP;
MP.reset();
vvc<int> states;
vc<pair<int, int>> edges;
states.eb(vc<int>(N, -1));
states.eb(vc<int>(N, -1));
MP[hash_vector<int>(states[0])] = 0;
int p = -1;
while (1) {
if (++p == len(states)) break;
if (p == 1) {
edges.eb(1, 1);
continue;
}
vc<int> now = states[p];
for (auto&& [nxt, convert]: next_states(now)) {
// 今の成分数、消える成分数
int a = 0, b = 0;
FOR(v, N) if (now[v] == v) {
++a;
if (convert[v] == -1) ++b;
}
// 消える成分があってよいのは、終状態にいくときのみ
if (b >= 2) continue;
if (b == 1) {
if (MAX(nxt) != -1) continue;
edges.eb(p, 1);
continue;
}
bool ok = [&]() -> bool {
// 頂点のみで接するのはダメ
FOR(i, N - 1) {
bool a1 = now[i] != -1, a2 = now[i + 1] != -1;
bool b1 = nxt[i] != -1, b2 = nxt[i + 1] != -1;
if (a1 && !a2 && !b1 && b2) return false;
if (!a1 && a2 && b1 && !b2) return false;
}
// empty region を閉じることと、異なる連結成分がマージされることが同値
int close = 0;
int after = 0;
vc<bool> is_new(N, 1);
FOR(i, N) if (convert[i] != -1) is_new[convert[i]] = 0;
FOR(i, N) if (nxt[i] == i && !is_new[i])++ after;
vc<int> I;
FOR(i, N) if (now[i] != -1) I.eb(i);
FOR(k, len(I) - 1) {
int i = I[k], j = I[k + 1];
if (j == i + 1) continue;
bool cl = 1;
FOR(p, i + 1, j) if (nxt[p] == -1) cl = 0;
if (cl) close++;
}
return a - close == after;
}();
if (!ok) continue;
ll h = hash_vector<int>(nxt);
if (!MP.count(h)) {
MP[h] = len(states);
states.eb(nxt);
}
edges.eb(p, MP[h]);
}
}
return {states, edges};
}
} // namespace connected_dp_squares
#line 2 "/home/maspy/compro/library/seq/interpolate_linear_rec.hpp"
#line 2 "/home/maspy/compro/library/seq/find_linear_rec.hpp"
template <typename mint>
vector<mint> find_linear_rec(vector<mint>& A) {
int N = len(A);
vc<mint> B = {1}, C = {1};
int l = 0, m = 1;
mint p = 1;
FOR(i, N) {
mint d = A[i];
FOR3(j, 1, l + 1) { d += C[j] * A[i - j]; }
if (d == 0) {
++m;
continue;
}
auto tmp = C;
mint q = d / p;
if (len(C) < len(B) + m) C.insert(C.end(), len(B) + m - len(C), 0);
FOR(j, len(B)) C[j + m] -= q * B[j];
if (l + l <= i) {
B = tmp;
l = i + 1 - l, m = 1;
p = d;
} else {
++m;
}
}
return C;
}
#line 2 "/home/maspy/compro/library/mod/mod_inv.hpp"
// long でも大丈夫
ll mod_inv(ll val, ll mod) {
val %= mod;
if (val < 0) val += mod;
ll 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);
}
if (u < 0) u += mod;
return u;
}
#line 1 "/home/maspy/compro/library/poly/convolution_naive.hpp"
template <class T>
vector<T> convolution_naive(const vector<T>& a, const vector<T>& b) {
int n = int(a.size()), m = int(b.size());
vector<T> ans(n + m - 1);
if (n < m) {
FOR(j, m) FOR(i, n) ans[i + j] += a[i] * b[j];
} else {
FOR(i, n) FOR(j, m) ans[i + j] += a[i] * b[j];
}
return ans;
}
#line 2 "/home/maspy/compro/library/poly/ntt.hpp"
template <class mint>
struct ntt_info {
static constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
static constexpr int rank2 = bsf_constexpr(mint::get_mod() - 1);
array<mint, rank2 + 1> root;
array<mint, rank2 + 1> iroot;
array<mint, max(0, rank2 - 1)> rate2;
array<mint, max(0, rank2 - 1)> irate2;
array<mint, max(0, rank2 - 2)> rate3;
array<mint, max(0, rank2 - 2)> irate3;
ntt_info() {
int g = primitive_root(mint::get_mod());
root[rank2] = mint(g).pow((mint::get_mod() - 1) >> rank2);
iroot[rank2] = mint(1) / root[rank2];
FOR_R(i, rank2) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 2; i++) {
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 3; i++) {
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
}
constexpr int primitive_root(int m) {
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 880803841) return 26;
if (m == 998244353) return 3;
if (m == 924844053) return 5;
return -1;
}
};
template <class mint>
void ntt(vector<mint>& a, bool inverse) {
int n = int(a.size());
int h = topbit(n);
assert(n == 1 << h);
static const ntt_info<mint> info;
if (!inverse) {
int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
mint rot = 1;
FOR(s, 1 << len) {
int offset = s << (h - len);
FOR(i, p) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
rot *= info.rate2[topbit(~s & -~s)];
}
len++;
} else {
int p = 1 << (h - len - 2);
mint rot = 1, imag = info.root[2];
for (int s = 0; s < (1 << len); s++) {
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto mod2 = 1ULL * mint::get_mod() * mint::get_mod();
auto a0 = 1ULL * a[i + offset].val;
auto a1 = 1ULL * a[i + offset + p].val * rot.val;
auto a2 = 1ULL * a[i + offset + 2 * p].val * rot2.val;
auto a3 = 1ULL * a[i + offset + 3 * p].val * rot3.val;
auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val * imag.val;
auto na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
rot *= info.rate3[topbit(~s & -~s)];
}
len += 2;
}
}
} else {
mint coef = mint(1) / mint(len(a));
FOR(i, len(a)) a[i] *= coef;
int len = h;
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
FOR(s, 1 << (len - 1)) {
int offset = s << (h - len + 1);
FOR(i, p) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p]
= (unsigned long long)(mint::get_mod() + l.val - r.val)
* irot.val;
;
}
irot *= info.irate2[topbit(~s & -~s)];
}
len--;
} else {
int p = 1 << (h - len);
mint irot = 1, iimag = info.iroot[2];
FOR(s, (1 << (len - 2))) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
auto a0 = 1ULL * a[i + offset + 0 * p].val;
auto a1 = 1ULL * a[i + offset + 1 * p].val;
auto a2 = 1ULL * a[i + offset + 2 * p].val;
auto a3 = 1ULL * a[i + offset + 3 * p].val;
auto a2na3iimag
= 1ULL * mint((mint::get_mod() + a2 - a3) * iimag.val).val;
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p]
= (a0 + (mint::get_mod() - a1) + a2na3iimag) * irot.val;
a[i + offset + 2 * p]
= (a0 + a1 + (mint::get_mod() - a2) + (mint::get_mod() - a3))
* irot2.val;
a[i + offset + 3 * p]
= (a0 + (mint::get_mod() - a1) + (mint::get_mod() - a2na3iimag))
* irot3.val;
}
irot *= info.irate3[topbit(~s & -~s)];
}
len -= 2;
}
}
}
}
#line 1 "/home/maspy/compro/library/poly/fft.hpp"
namespace CFFT {
using real = double;
struct C {
real x, y;
C() : x(0), y(0) {}
C(real x, real y) : x(x), y(y) {}
inline C operator+(const C& c) const { return C(x + c.x, y + c.y); }
inline C operator-(const C& c) const { return C(x - c.x, y - c.y); }
inline C operator*(const C& c) const {
return C(x * c.x - y * c.y, x * c.y + y * c.x);
}
inline C conj() const { return C(x, -y); }
};
const real PI = acosl(-1);
int base = 1;
vector<C> rts = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};
void ensure_base(int nbase) {
if (nbase <= base) return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for (int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
while (base < nbase) {
real angle = PI * 2.0 / (1 << (base + 1));
for (int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
real angle_i = angle * (2 * i + 1 - (1 << base));
rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
}
++base;
}
}
void fft(vector<C>& a, int n) {
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for (int i = 0; i < n; i++) {
if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); }
}
for (int k = 1; k < n; k <<= 1) {
for (int i = 0; i < n; i += 2 * k) {
for (int j = 0; j < k; j++) {
C z = a[i + j + k] * rts[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
} // namespace CFFT
#line 7 "/home/maspy/compro/library/poly/convolution.hpp"
template <class mint>
vector<mint> convolution_ntt(vector<mint> a, vector<mint> b) {
int n = int(a.size()), m = int(b.size());
int sz = 1;
while (sz < n + m - 1) sz *= 2;
// sz = 2^k のときの高速化。分割統治的なやつで損しまくるので。
if ((n + m - 3) <= sz / 2) {
auto a_last = a.back(), b_last = b.back();
a.pop_back(), b.pop_back();
auto c = convolution(a, b);
c.resize(n + m - 1);
c[n + m - 2] = a_last * b_last;
FOR(i, len(a)) c[i + len(b)] += a[i] * b_last;
FOR(i, len(b)) c[i + len(a)] += b[i] * a_last;
return c;
}
a.resize(sz), b.resize(sz);
bool same = a == b;
ntt(a, 0);
if (same) {
b = a;
} else {
ntt(b, 0);
}
FOR(i, sz) a[i] *= b[i];
ntt(a, 1);
a.resize(n + m - 1);
return a;
}
template <typename mint>
vector<mint> convolution_garner(const vector<mint>& a, const vector<mint>& b) {
int n = len(a), m = len(b);
if (!n || !m) return {};
static const long long nttprimes[] = {754974721, 167772161, 469762049};
using mint0 = modint<754974721>;
using mint1 = modint<167772161>;
using mint2 = modint<469762049>;
vc<mint0> a0(n), b0(m);
vc<mint1> a1(n), b1(m);
vc<mint2> a2(n), b2(m);
FOR(i, n) a0[i] = a[i].val, a1[i] = a[i].val, a2[i] = a[i].val;
FOR(i, m) b0[i] = b[i].val, b1[i] = b[i].val, b2[i] = b[i].val;
auto c0 = convolution_ntt<mint0>(a0, b0);
auto c1 = convolution_ntt<mint1>(a1, b1);
auto c2 = convolution_ntt<mint2>(a2, b2);
static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
static const long long m0_inv_m1 = mint1(nttprimes[0]).inverse().val;
static const long long m01_inv_m2 = mint2(m01).inverse().val;
static const int mod = mint::get_mod();
auto garner = [&](mint0 x0, mint1 x1, mint2 x2) -> mint {
int r0 = x0.val, r1 = x1.val, r2 = x2.val;
int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * mint2(m01_inv_m2);
return mint(r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val);
};
vc<mint> c(len(c0));
FOR(i, len(c)) c[i] = garner(c0[i], c1[i], c2[i]);
return c;
}
template <typename R>
vc<double> convolution_fft(const vc<R>& a, const vc<R>& b) {
using C = CFFT::C;
int need = (int)a.size() + (int)b.size() - 1;
int nbase = 1;
while ((1 << nbase) < need) nbase++;
CFFT::ensure_base(nbase);
int sz = 1 << nbase;
vector<C> fa(sz);
for (int i = 0; i < sz; i++) {
int x = (i < (int)a.size() ? a[i] : 0);
int y = (i < (int)b.size() ? b[i] : 0);
fa[i] = C(x, y);
}
CFFT::fft(fa, sz);
C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
for (int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
fa[i] = z;
}
for (int i = 0; i < (sz >> 1); i++) {
C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * CFFT::rts[(sz >> 1) + i];
fa[i] = A0 + A1 * s;
}
CFFT::fft(fa, sz >> 1);
vector<double> ret(need);
for (int i = 0; i < need; i++) {
ret[i] = (i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
}
return ret;
}
vector<ll> convolution(const vector<ll>& a, const vector<ll>& b) {
int n = len(a), m = len(b);
if (!n || !m) return {};
if (min(n, m) <= 60) return convolution_naive(a, b);
ll abs_sum_a = 0, abs_sum_b = 0;
ll LIM = 1e15;
FOR(i, n) abs_sum_a = min(LIM, abs_sum_a + abs(a[i]));
FOR(i, n) abs_sum_b = min(LIM, abs_sum_b + abs(b[i]));
if (i128(abs_sum_a) * abs_sum_b < 1e15) {
vc<double> c = convolution_fft<ll>(a, b);
vc<ll> res(len(c));
FOR(i, len(c)) res[i] = ll(floor(c[i] + .5));
return res;
}
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static const unsigned long long i1 = mod_inv(MOD2 * MOD3, MOD1);
static const unsigned long long i2 = mod_inv(MOD1 * MOD3, MOD2);
static const unsigned long long i3 = mod_inv(MOD1 * MOD2, MOD3);
using mint1 = modint<MOD1>;
using mint2 = modint<MOD2>;
using mint3 = modint<MOD3>;
vc<mint1> a1(n), b1(m);
vc<mint2> a2(n), b2(m);
vc<mint3> a3(n), b3(m);
FOR(i, n) a1[i] = a[i], a2[i] = a[i], a3[i] = a[i];
FOR(i, m) b1[i] = b[i], b2[i] = b[i], b3[i] = b[i];
auto c1 = convolution_ntt<mint1>(a1, b1);
auto c2 = convolution_ntt<mint2>(a2, b2);
auto c3 = convolution_ntt<mint3>(a3, b3);
vc<ll> c(n + m - 1);
FOR(i, n + m - 1) {
u64 x = 0;
x += (c1[i].val * i1) % MOD1 * M2M3;
x += (c2[i].val * i2) % MOD2 * M1M3;
x += (c3[i].val * i3) % MOD3 * M1M2;
ll diff = c1[i].val - ((long long)(x) % (long long)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr unsigned long long offset[5]
= {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
template <typename mint>
enable_if_t<is_same<mint, modint998>::value, vc<mint>> convolution(
const vc<mint>& a, const vc<mint>& b) {
int n = len(a), m = len(b);
if (!n || !m) return {};
if (min(n, m) <= 60) return convolution_naive(a, b);
return convolution_ntt(a, b);
}
template <typename mint>
enable_if_t<!is_same<mint, modint998>::value, vc<mint>> convolution(
const vc<mint>& a, const vc<mint>& b) {
int n = len(a), m = len(b);
if (!n || !m) return {};
if (min(n, m) <= 60) return convolution_naive(a, b);
return convolution_garner(a, b);
}
#line 2 "/home/maspy/compro/library/poly/coef_of_rational_fps.hpp"
template <typename mint>
mint coef_of_rational_fps(vector<mint> A, vector<mint> B, ll N) {
if (len(A) == 0) return 0;
assert(len(A) < len(B));
while (len(A) + 1 < len(B)) A.eb(0);
assert(B[0] == mint(1));
assert(len(B) == len(A) + 1);
while (N) {
vc<mint> B1 = B;
FOR(i, len(B1)) if (i & 1) B1[i] = -B1[i];
A = convolution(A, B1);
B = convolution(B, B1);
FOR(i, len(B1)) B[i] = B[2 * i];
if (N & 1) {
FOR(i, len(B1) - 1) A[i] = A[2 * i | 1];
} else {
FOR(i, len(B1) - 1) A[i] = A[2 * i];
}
A.resize(len(B1) - 1);
B.resize(len(B1));
N /= 2;
}
return A[0];
}
#line 5 "/home/maspy/compro/library/seq/interpolate_linear_rec.hpp"
template <typename mint>
mint interpolate_linear_rec(vector<mint>& A, ll N, int off) {
if(N < len(A)) return A[N];
A = {A.begin() + off, A.end()};
N -= off;
auto G = find_linear_rec(A);
auto F = convolution(A, G);
F.resize(len(G) - 1);
return coef_of_rational_fps(F, G, N);
}
#line 7 "main.cpp"
using mint = modint107;
void solve() {
LL(N);
auto [states, edges] = connected_dp_squares::polygon_dp_graph(3);
const int S = len(states);
int E = len(edges);
vc<int> count_line(E);
FOR(e, E) {
auto& now = states[edges[e].fi];
auto& nxt = states[edges[e].se];
int n = 0;
FOR(i, len(now)) {
if ((now[i] == -1) != (nxt[i] == -1)) ++n;
}
FOR(i, len(nxt) + 1) {
bool a = (i == 0 ? 0 : nxt[i - 1] != -1);
bool b = (i == len(nxt) ? 0 : nxt[i] != -1);
if (a != b) ++n;
}
count_line[e] = n;
}
const int LIM = 4 * S + 10;
// 辺を選んだ、選んでいない
vv(mint, dp, 2, S);
vc<mint> f(LIM);
dp[0][0] = 1;
FOR(i, LIM) {
vv(mint, newdp, 2, S);
FOR(e, E) {
auto [a, b] = edges[e];
newdp[0][b] += dp[0][a];
newdp[1][b] += dp[1][a];
newdp[1][b] += dp[0][a] * mint(count_line[e]);
}
swap(dp, newdp);
f[i] = dp[1][1];
}
mint ANS = interpolate_linear_rec<mint>(f, N, 0);
print(ANS);
}
signed main() {
cout << fixed << setprecision(15);
ll T = 1;
// LL(T);
FOR(T) solve();
return 0;
}