結果
| 問題 | No.2959 Dolls' Tea Party |
| ユーザー |
 hirayuu_yc
|
| 提出日時 | 2024-11-08 23:10:33 |
| 言語 | C++23(gcc13) (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 2,810 ms / 3,000 ms |
| コード長 | 27,561 bytes |
| コンパイル時間 | 4,895 ms |
| コンパイル使用メモリ | 310,112 KB |
| 実行使用メモリ | 6,016 KB |
| 最終ジャッジ日時 | 2024-11-08 23:11:41 |
| 合計ジャッジ時間 | 54,932 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 | 2 ms
5,248 KB |
| testcase_05 | AC | 2 ms
5,248 KB |
| testcase_06 | AC | 475 ms
5,760 KB |
| testcase_07 | AC | 507 ms
6,016 KB |
| testcase_08 | AC | 475 ms
5,760 KB |
| testcase_09 | AC | 2,810 ms
6,016 KB |
| testcase_10 | AC | 2,750 ms
6,016 KB |
| testcase_11 | AC | 2,775 ms
6,016 KB |
| testcase_12 | AC | 2,742 ms
5,888 KB |
| testcase_13 | AC | 2,747 ms
5,888 KB |
| testcase_14 | AC | 581 ms
5,760 KB |
| testcase_15 | AC | 517 ms
5,760 KB |
| testcase_16 | AC | 2,730 ms
5,888 KB |
| testcase_17 | AC | 2,709 ms
5,888 KB |
| testcase_18 | AC | 2,729 ms
6,016 KB |
| testcase_19 | AC | 2,707 ms
5,888 KB |
| testcase_20 | AC | 2,715 ms
6,016 KB |
| testcase_21 | AC | 2,582 ms
5,888 KB |
| testcase_22 | AC | 2,537 ms
6,016 KB |
| testcase_23 | AC | 2,531 ms
5,888 KB |
| testcase_24 | AC | 2 ms
5,248 KB |
| testcase_25 | AC | 2 ms
5,248 KB |
| testcase_26 | AC | 2 ms
5,248 KB |
| testcase_27 | AC | 414 ms
5,248 KB |
| testcase_28 | AC | 440 ms
5,248 KB |
| testcase_29 | AC | 468 ms
5,760 KB |
| testcase_30 | AC | 339 ms
5,888 KB |
| testcase_31 | AC | 347 ms
5,632 KB |
| testcase_32 | AC | 1,726 ms
6,016 KB |
| testcase_33 | AC | 1,825 ms
5,888 KB |
| testcase_34 | AC | 1,858 ms
6,016 KB |
| testcase_35 | AC | 1,898 ms
5,888 KB |
| testcase_36 | AC | 1,711 ms
5,888 KB |
ソースコード
#line 2 "/root/AtCoder/Halc-Library/Template/Template.hpp"
#include <bits/stdc++.h>
using namespace std;
#line 8 "/root/AtCoder/Halc-Library/Template/InOut.hpp"
inline void scan() {}
inline void scan(int32_t &a) { std::cin >> a; }
inline void scan(uint32_t &a) { std::cin >> a; }
inline void scan(int64_t &a) { std::cin >> a; }
inline void scan(uint64_t &a) { std::cin >> a; }
inline void scan(char &a) { std::cin >> a; }
inline void scan(float &a) { std::cin >> a; }
inline void scan(double &a) { std::cin >> a; }
inline void scan(long double &a) { std::cin >> a; }
inline void scan(std::vector<bool> &vec) {
for (int32_t i = 0; i < vec.size(); i++) {
int a;
scan(a);
vec[i] = a;
}
}
inline void scan(std::string &a) { std::cin >> a; }
template <class T>
inline void scan(std::vector<T> &vec);
template <class T, size_t size>
inline void scan(std::array<T, size> &vec);
template <class T, class L>
inline void scan(std::pair<T, L> &p);
template <class T, size_t size>
inline void scan(T (&vec)[size]);
template <class T>
inline void scan(std::vector<T> &vec) {
for (auto &i : vec) scan(i);
}
template <class T>
inline void scan(std::deque<T> &vec) {
for (auto &i : vec) scan(i);
}
template <class T, size_t size>
inline void scan(std::array<T, size> &vec) {
for (auto &i : vec) scan(i);
}
template <class T, class L>
inline void scan(std::pair<T, L> &p) {
scan(p.first);
scan(p.second);
}
template <class T, size_t size>
inline void scan(T (&vec)[size]) {
for (auto &i : vec) scan(i);
}
template <class T>
inline void scan(T &a) {
std::cin >> a;
}
inline void in() {}
template <class Head, class... Tail>
inline void in(Head &head, Tail &...tail) {
scan(head);
in(tail...);
}
inline void print() { std::cout << ' '; }
inline void print(const bool &a) { std::cout << a; }
inline void print(const int32_t &a) { std::cout << a; }
inline void print(const uint32_t &a) { std::cout << a; }
inline void print(const int64_t &a) { std::cout << a; }
inline void print(const uint64_t &a) { std::cout << a; }
inline void print(const char &a) { std::cout << a; }
inline void print(const char a[]) { std::cout << a; }
inline void print(const float &a) { std::cout << a; }
inline void print(const double &a) { std::cout << a; }
inline void print(const long double &a) { std::cout << a; }
inline void print(const std::string &a) {
for (auto &&i : a) print(i);
}
template <class T>
inline void print(const std::vector<T> &vec);
template <class T, size_t size>
inline void print(const std::array<T, size> &vec);
template <class T, class L>
inline void print(const std::pair<T, L> &p);
template <class T, size_t size>
inline void print(const T (&vec)[size]);
template <class T>
inline void print(const std::vector<T> &vec) {
if (vec.empty()) return;
print(vec[0]);
for (auto i = vec.begin(); ++i != vec.end();) {
std::cout << ' ';
print(*i);
}
}
template <class T>
inline void print(const std::deque<T> &vec) {
if (vec.empty()) return;
print(vec[0]);
for (auto i = vec.begin(); ++i != vec.end();) {
std::cout << ' ';
print(*i);
}
}
template <class T, size_t size>
inline void print(const std::array<T, size> &vec) {
print(vec[0]);
for (auto i = vec.begin(); ++i != vec.end();) {
std::cout << ' ';
print(*i);
}
}
template <class T, class L>
inline void print(const std::pair<T, L> &p) {
print(p.first);
std::cout << ' ';
print(p.second);
}
template <class T, size_t size>
inline void print(const T (&vec)[size]) {
print(vec[0]);
for (auto i = vec; ++i != end(vec);) {
std::cout << ' ';
print(*i);
}
}
template <class T>
inline void print(const T &a) {
std::cout << a;
}
inline void out() { std::cout << '\n'; }
template <class T>
inline void out(const T &t) {
print(t);
std::cout << '\n';
}
template <class Head, class... Tail>
inline void out(const Head &head, const Tail &...tail) {
print(head);
std::cout << ' ';
out(tail...);
}
inline void Yes(bool i = true) { out(i ? "Yes" : "No"); }
inline void No(bool i = true) { out(i ? "No" : "Yes"); }
inline void Takahashi(bool i = true) { out(i ? "Takahashi" : "Aoki"); }
inline void Aoki(bool i = true) { out(i ? "Aoki" : "Takahashi"); }
inline void Alice(bool i = true) { out(i ? "Alice" : "Bob"); }
inline void Bob(bool i = true) { out(i ? "Bob" : "Alice"); }
inline void First(bool i = true) { out(i ? "First" : "Second"); }
inline void Second(bool i = true) { out(i ? "Second" : "First"); }
inline void Possible(bool i = true) { out(i ? "Possible" : "Impossible"); }
inline void Impossible(bool i = true) { out(i ? "Impossible" : "Possible"); }
inline void fls() { std::flush(std::cout); }
struct IOsetup {
IOsetup() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(16);
}
} iosetup;
#line 9 "/root/AtCoder/Halc-Library/Template/Util.hpp"
using ll = int64_t;
using ld = long double;
using ull = uint64_t;
using uint = uint32_t;
using pll = std::pair<ll, ll>;
using pii = std::pair<int32_t, int32_t>;
using vl = std::vector<ll>;
using vvl = std::vector<std::vector<ll>>;
using pdd = std::pair<ld, ld>;
using tuplis = std::array<ll, 3>;
template <class T>
using pq = std::priority_queue<T, std::vector<T>, std::greater<T>>;
constexpr ll LINF = (1LL << 62) - (1LL << 31);
constexpr int32_t INF = INT_MAX >> 1;
constexpr ll MINF = 1LL << 40;
constexpr ld DINF = std::numeric_limits<ld>::infinity();
constexpr int32_t MODD = 1000000007;
constexpr int32_t MOD = 998244353;
constexpr ld EPS = 1e-9;
constexpr ld PI = 3.1415926535897932;
const ll four[] = {0, 1, 0, -1, 0};
const ll eight[] = {0, 1, 1, 0, -1, -1, 1, -1, 0};
template <class T>
bool chmin(T &a, const T &b) {
if (a > b) {
a = b;
return true;
} else
return false;
}
template <class T>
bool chmax(T &a, const T &b) {
if (a < b) {
a = b;
return true;
} else
return false;
}
template <class T>
ll sum(const T &a) {
return accumulate(std::begin(a), std::end(a), 0LL);
}
template <class T>
ld dsum(const T &a) {
return accumulate(std::begin(a), std::end(a), 0.0L);
}
template <class T>
auto min(const T &a) {
return *min_element(std::begin(a), std::end(a));
}
template <class T>
auto max(const T &a) {
return *max_element(std::begin(a), std::end(a));
}
#line 1 "/root/AtCoder/Halc-Library/Template/Macro.hpp"
#define _overload3(_1, _2, _3, name, ...) name
#define _overload4(_1, _2, _3, _4, name, ...) name
#define _rep1(i, n) for (int64_t i = 0; i < (n); i++)
#define _rep2(i, a, b) for (int64_t i = (a); i < (b); i++)
#define _rep3(i, a, b, c) for (int64_t i = (a); i < (b); i += (c))
#define rep(...) _overload4(__VA_ARGS__, _rep3, _rep2, _rep1)(__VA_ARGS__)
#define _rrep1(i, n) for (int64_t i = (n) - 1; i >= 0; i--)
#define _rrep2(i, a, b) for (int64_t i = (b) - 1; i >= (a); i--)
#define rrep(...) _overload3(__VA_ARGS__, _rrep2, _rrep1)(__VA_ARGS__)
#define each(i, ...) for (auto&& i : __VA_ARGS__)
#define all(i) std::begin(i), std::end(i)
#define rall(i) std::rbegin(i), std::rend(i)
#define len(x) ((int64_t)(x).size())
#define fi first
#define se second
#define uniq(x) x.erase(unique(all(x)), std::end(x))
#define vec(type, name, ...) vector<type> name(__VA_ARGS__);
#define vv(type, name, h, ...) std::vector<std::vector<type>> name(h, std::vector<type>(__VA_ARGS__));
#define INT(...) int32_t __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) int64_t __VA_ARGS__; in(__VA_ARGS__)
#define ULL(...) uint64_t __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) std::string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) long double __VA_ARGS__; in(__VA_ARGS__)
#define VEC(type, name, size) std::vector<type> name(size); in(name)
#define VV(type, name, h, w) std::vector<std::vector<type>> name(h, std::vector<type>(w)); in(name)
#line 4 "/root/AtCoder/Halc-Library/Math/ModCombination.hpp"
template <typename T>
struct ModCombination {
std::vector<T> fact = {1}, rev{1};
ModCombination(uint32_t sz = 0) {
fact.reserve(sz+1);
rev.reserve(sz+1);
}
void resize(uint32_t sz) {
sz++;
if (fact.size() >= sz) return;
uint32_t before = fact.size();
fact.resize(sz);
rev.resize(sz);
for (uint32_t i = before; i < sz; i++) {
fact[i] = fact[i - 1] * i;
rev[i] = rev[i - 1] / i;
}
}
T comb(int32_t n, int32_t k) {
if (n < 0 || k < 0 || n < k) return 0;
resize(n);
return fact[n] * rev[n - k] * rev[k];
}
T perm(int32_t n, int32_t k) {
if (n < 0 || k < 0 || n < k) return 0;
resize(n);
return fact[n] * rev[n - k];
}
T multi_comb(int32_t n, int32_t k) {
if (k == 0) return 1;
return comb(n + k - 1, k);
}
};
#line 3 "main.cpp"
#line 2 "fps/ntt-friendly-fps.hpp"
#line 2 "ntt/ntt.hpp"
template <typename mint>
struct NTT {
static constexpr uint32_t get_pr() {
uint32_t _mod = mint::get_mod();
using u64 = uint64_t;
u64 ds[32] = {};
int idx = 0;
u64 m = _mod - 1;
for (u64 i = 2; i * i <= m; ++i) {
if (m % i == 0) {
ds[idx++] = i;
while (m % i == 0) m /= i;
}
}
if (m != 1) ds[idx++] = m;
uint32_t _pr = 2;
while (1) {
int flg = 1;
for (int i = 0; i < idx; ++i) {
u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
while (b) {
if (b & 1) r = r * a % _mod;
a = a * a % _mod;
b >>= 1;
}
if (r == 1) {
flg = 0;
break;
}
}
if (flg == 1) break;
++_pr;
}
return _pr;
};
static constexpr uint32_t mod = mint::get_mod();
static constexpr uint32_t pr = get_pr();
static constexpr int level = __builtin_ctzll(mod - 1);
mint dw[level], dy[level];
void setwy(int k) {
mint w[level], y[level];
w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
y[k - 1] = w[k - 1].inverse();
for (int i = k - 2; i > 0; --i)
w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
for (int i = 3; i < k; ++i) {
dw[i] = dw[i - 1] * y[i - 2] * w[i];
dy[i] = dy[i - 1] * w[i - 2] * y[i];
}
}
NTT() { setwy(level); }
void fft4(vector<mint> &a, int k) {
if ((int)a.size() <= 1) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
if (k & 1) {
int v = 1 << (k - 1);
for (int j = 0; j < v; ++j) {
mint ajv = a[j + v];
a[j + v] = a[j] - ajv;
a[j] += ajv;
}
}
int u = 1 << (2 + (k & 1));
int v = 1 << (k - 2 - (k & 1));
mint one = mint(1);
mint imag = dw[1];
while (v) {
// jh = 0
{
int j0 = 0;
int j1 = v;
int j2 = j1 + v;
int j3 = j2 + v;
for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
}
}
// jh >= 1
mint ww = one, xx = one * dw[2], wx = one;
for (int jh = 4; jh < u;) {
ww = xx * xx, wx = ww * xx;
int j0 = jh * v;
int je = j0 + v;
int j2 = je + v;
for (; j0 < je; ++j0, ++j2) {
mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
t3 = a[j2 + v] * wx;
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
}
xx *= dw[__builtin_ctzll((jh += 4))];
}
u <<= 2;
v >>= 2;
}
}
void ifft4(vector<mint> &a, int k) {
if ((int)a.size() <= 1) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
int u = 1 << (k - 2);
int v = 1;
mint one = mint(1);
mint imag = dy[1];
while (u) {
// jh = 0
{
int j0 = 0;
int j1 = v;
int j2 = v + v;
int j3 = j2 + v;
for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
}
}
// jh >= 1
mint ww = one, xx = one * dy[2], yy = one;
u <<= 2;
for (int jh = 4; jh < u;) {
ww = xx * xx, yy = xx * imag;
int j0 = jh * v;
int je = j0 + v;
int j2 = je + v;
for (; j0 < je; ++j0, ++j2) {
mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
}
xx *= dy[__builtin_ctzll(jh += 4)];
}
u >>= 4;
v <<= 2;
}
if (k & 1) {
u = 1 << (k - 1);
for (int j = 0; j < u; ++j) {
mint ajv = a[j] - a[j + u];
a[j] += a[j + u];
a[j + u] = ajv;
}
}
}
void ntt(vector<mint> &a) {
if ((int)a.size() <= 1) return;
fft4(a, __builtin_ctz(a.size()));
}
void intt(vector<mint> &a) {
if ((int)a.size() <= 1) return;
ifft4(a, __builtin_ctz(a.size()));
mint iv = mint(a.size()).inverse();
for (auto &x : a) x *= iv;
}
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
int l = a.size() + b.size() - 1;
if (min<int>(a.size(), b.size()) <= 40) {
vector<mint> s(l);
for (int i = 0; i < (int)a.size(); ++i)
for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
return s;
}
int k = 2, M = 4;
while (M < l) M <<= 1, ++k;
setwy(k);
vector<mint> s(M);
for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
fft4(s, k);
if (a.size() == b.size() && a == b) {
for (int i = 0; i < M; ++i) s[i] *= s[i];
} else {
vector<mint> t(M);
for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
fft4(t, k);
for (int i = 0; i < M; ++i) s[i] *= t[i];
}
ifft4(s, k);
s.resize(l);
mint invm = mint(M).inverse();
for (int i = 0; i < l; ++i) s[i] *= invm;
return s;
}
void ntt_doubling(vector<mint> &a) {
int M = (int)a.size();
auto b = a;
intt(b);
mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;
ntt(b);
copy(begin(b), end(b), back_inserter(a));
}
};
#line 2 "fps/formal-power-series.hpp"
template <typename mint>
struct FormalPowerSeries : vector<mint> {
using vector<mint>::vector;
using FPS = FormalPowerSeries;
FPS &operator+=(const FPS &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
return *this;
}
FPS &operator+=(const mint &r) {
if (this->empty()) this->resize(1);
(*this)[0] += r;
return *this;
}
FPS &operator-=(const FPS &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
return *this;
}
FPS &operator-=(const mint &r) {
if (this->empty()) this->resize(1);
(*this)[0] -= r;
return *this;
}
FPS &operator*=(const mint &v) {
for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;
return *this;
}
FPS &operator/=(const FPS &r) {
if (this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
if ((int)r.size() <= 64) {
FPS f(*this), g(r);
g.shrink();
mint coeff = g.back().inverse();
for (auto &x : g) x *= coeff;
int deg = (int)f.size() - (int)g.size() + 1;
int gs = g.size();
FPS quo(deg);
for (int i = deg - 1; i >= 0; i--) {
quo[i] = f[i + gs - 1];
for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];
}
*this = quo * coeff;
this->resize(n, mint(0));
return *this;
}
return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
}
FPS &operator%=(const FPS &r) {
*this -= *this / r * r;
shrink();
return *this;
}
FPS operator+(const FPS &r) const { return FPS(*this) += r; }
FPS operator+(const mint &v) const { return FPS(*this) += v; }
FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
FPS operator-(const mint &v) const { return FPS(*this) -= v; }
FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
FPS operator*(const mint &v) const { return FPS(*this) *= v; }
FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
FPS operator-() const {
FPS ret(this->size());
for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
void shrink() {
while (this->size() && this->back() == mint(0)) this->pop_back();
}
FPS rev() const {
FPS ret(*this);
reverse(begin(ret), end(ret));
return ret;
}
FPS dot(FPS r) const {
FPS ret(min(this->size(), r.size()));
for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];
return ret;
}
// 前 sz 項を取ってくる。sz に足りない項は 0 埋めする
FPS pre(int sz) const {
FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz));
if ((int)ret.size() < sz) ret.resize(sz);
return ret;
}
FPS operator>>(int sz) const {
if ((int)this->size() <= sz) return {};
FPS ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
FPS operator<<(int sz) const {
FPS ret(*this);
ret.insert(ret.begin(), sz, mint(0));
return ret;
}
FPS diff() const {
const int n = (int)this->size();
FPS ret(max(0, n - 1));
mint one(1), coeff(1);
for (int i = 1; i < n; i++) {
ret[i - 1] = (*this)[i] * coeff;
coeff += one;
}
return ret;
}
FPS integral() const {
const int n = (int)this->size();
FPS ret(n + 1);
ret[0] = mint(0);
if (n > 0) ret[1] = mint(1);
auto mod = mint::get_mod();
for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);
for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];
return ret;
}
mint eval(mint x) const {
mint r = 0, w = 1;
for (auto &v : *this) r += w * v, w *= x;
return r;
}
FPS log(int deg = -1) const {
assert(!(*this).empty() && (*this)[0] == mint(1));
if (deg == -1) deg = (int)this->size();
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
FPS pow(int64_t k, int deg = -1) const {
const int n = (int)this->size();
if (deg == -1) deg = n;
if (k == 0) {
FPS ret(deg);
if (deg) ret[0] = 1;
return ret;
}
for (int i = 0; i < n; i++) {
if ((*this)[i] != mint(0)) {
mint rev = mint(1) / (*this)[i];
FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
ret *= (*this)[i].pow(k);
ret = (ret << (i * k)).pre(deg);
if ((int)ret.size() < deg) ret.resize(deg, mint(0));
return ret;
}
if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));
}
return FPS(deg, mint(0));
}
static void *ntt_ptr;
static void set_fft();
FPS &operator*=(const FPS &r);
void ntt();
void intt();
void ntt_doubling();
static int ntt_pr();
FPS inv(int deg = -1) const;
FPS exp(int deg = -1) const;
};
template <typename mint>
void *FormalPowerSeries<mint>::ntt_ptr = nullptr;
/**
* @brief 多項式/形式的冪級数ライブラリ
* @docs docs/fps/formal-power-series.md
*/
#line 5 "fps/ntt-friendly-fps.hpp"
template <typename mint>
void FormalPowerSeries<mint>::set_fft() {
if (!ntt_ptr) ntt_ptr = new NTT<mint>;
}
template <typename mint>
FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(
const FormalPowerSeries<mint>& r) {
if (this->empty() || r.empty()) {
this->clear();
return *this;
}
set_fft();
auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r);
return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());
}
template <typename mint>
void FormalPowerSeries<mint>::ntt() {
set_fft();
static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);
}
template <typename mint>
void FormalPowerSeries<mint>::intt() {
set_fft();
static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);
}
template <typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
set_fft();
static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);
}
template <typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
set_fft();
return static_cast<NTT<mint>*>(ntt_ptr)->pr;
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
assert((*this)[0] != mint(0));
if (deg == -1) deg = (int)this->size();
FormalPowerSeries<mint> res(deg);
res[0] = {mint(1) / (*this)[0]};
for (int d = 1; d < deg; d <<= 1) {
FormalPowerSeries<mint> f(2 * d), g(2 * d);
for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j];
for (int j = 0; j < d; j++) g[j] = res[j];
f.ntt();
g.ntt();
for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
f.intt();
for (int j = 0; j < d; j++) f[j] = 0;
f.ntt();
for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
f.intt();
for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];
}
return res.pre(deg);
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
using fps = FormalPowerSeries<mint>;
assert((*this).size() == 0 || (*this)[0] == mint(0));
if (deg == -1) deg = this->size();
fps inv;
inv.reserve(deg + 1);
inv.push_back(mint(0));
inv.push_back(mint(1));
auto inplace_integral = [&](fps& F) -> void {
const int n = (int)F.size();
auto mod = mint::get_mod();
while ((int)inv.size() <= n) {
int i = inv.size();
inv.push_back((-inv[mod % i]) * (mod / i));
}
F.insert(begin(F), mint(0));
for (int i = 1; i <= n; i++) F[i] *= inv[i];
};
auto inplace_diff = [](fps& F) -> void {
if (F.empty()) return;
F.erase(begin(F));
mint coeff = 1, one = 1;
for (int i = 0; i < (int)F.size(); i++) {
F[i] *= coeff;
coeff += one;
}
};
fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
for (int m = 2; m < deg; m *= 2) {
auto y = b;
y.resize(2 * m);
y.ntt();
z1 = z2;
fps z(m);
for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i];
z.intt();
fill(begin(z), begin(z) + m / 2, mint(0));
z.ntt();
for (int i = 0; i < m; ++i) z[i] *= -z1[i];
z.intt();
c.insert(end(c), begin(z) + m / 2, end(z));
z2 = c;
z2.resize(2 * m);
z2.ntt();
fps x(begin(*this), begin(*this) + min<int>(this->size(), m));
x.resize(m);
inplace_diff(x);
x.push_back(mint(0));
x.ntt();
for (int i = 0; i < m; ++i) x[i] *= y[i];
x.intt();
x -= b.diff();
x.resize(2 * m);
for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0);
x.ntt();
for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i];
x.intt();
x.pop_back();
inplace_integral(x);
for (int i = m; i < min<int>(this->size(), 2 * m); ++i) x[i] += (*this)[i];
fill(begin(x), begin(x) + m, mint(0));
x.ntt();
for (int i = 0; i < 2 * m; ++i) x[i] *= y[i];
x.intt();
b.insert(end(b), begin(x) + m, end(x));
}
return fps{begin(b), begin(b) + deg};
}
/**
* @brief NTT mod用FPSライブラリ
* @docs docs/fps/ntt-friendly-fps.md
*/
#line 2 "modint/modint.hpp"
template <int mod>
struct ModInt {
int x;
ModInt() : x(0) {}
ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
ModInt &operator+=(const ModInt &p) {
if ((x += p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator-=(const ModInt &p) {
if ((x += mod - p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inverse();
return *this;
}
ModInt operator-() const { return ModInt(-x); }
ModInt operator+() const { return ModInt(*this); }
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 x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inverse() const {
int 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);
}
return ModInt(u);
}
ModInt pow(int64_t n) const {
ModInt ret(1), mul(x);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
friend istream &operator>>(istream &is, ModInt &a) {
int64_t t;
is >> t;
a = ModInt<mod>(t);
return (is);
}
int get() const { return x; }
static constexpr int get_mod() { return mod; }
};
/**
* @brief modint
*/
using mint=ModInt<MOD>;
ModCombination<mint> cb;
using fps = FormalPowerSeries<mint>;
void solve() {
LL(N,K);
VEC(ll,A,N);
vec(mint,memo,K+1);
mint ans=0;
cb.resize(K+100);
rep(i,1,K+1){
ll g=gcd(i,K);
if(g!=i){
ans+=memo[g];
continue;
}
ll backet=K/g;
vl cnt(g+1);
rep(j,N){
cnt[min(g,A[j]/backet)]++;
}
fps s={cb.fact[g]};
fps now={};
now.reserve(g+1);
rep(j,g+1){
now.push_back(cb.rev[j]);
s*=now.pow(cnt[j],g+1);
while(len(s)>g+1)s.pop_back();
}
ans+=s[g];
memo[g]=s[g];
}
out(ans/K);
}
int main() { solve(); }
/*---------------------✂ｷﾘﾄﾘ線✂----------------------*\
| Coding by hirayuu_At. |
| |
| ( ﾟдﾟ) |
| ＿(__つ/￣￣￣/＿ ∧∧ |
| ＼/ WA / /⌒ヽ) |
| ￣￣￣ ／＼ i三 ∪ |
| . ∵ .／ .／| 〇三 | |
| ∴ ＼／ ／ (/~∪ |
| (ﾉﾟДﾟ)ﾉ |／ 三三 終 |
| / / 三三 制作・著作 |
| ￣￣￣￣￣￣ 三三三 ━━━━━━━━━━ |
| ⒽⒶⓁⒸ |
\*-----------------------✂ｷﾘﾄﾘ線✂--------------------*/