結果
| 問題 | No.1956 猫の額 |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2022-05-24 02:08:04 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 29,109 bytes |
| コンパイル時間 | 4,368 ms |
| コンパイル使用メモリ | 262,448 KB |
| 実行使用メモリ | 4,552 KB |
| 最終ジャッジ日時 | 2023-10-20 18:41:39 |
| 合計ジャッジ時間 | 5,423 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge12 |
（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 | WA | - |
| testcase_01 | WA | - |
| testcase_02 | WA | - |
| testcase_03 | WA | - |
| testcase_04 | WA | - |
| testcase_05 | WA | - |
| testcase_06 | WA | - |
| testcase_07 | WA | - |
| testcase_08 | AC | 7 ms
4,348 KB |
| testcase_09 | AC | 7 ms
4,348 KB |
| testcase_10 | AC | 7 ms
4,348 KB |
| testcase_11 | AC | 5 ms
4,348 KB |
| testcase_12 | AC | 5 ms
4,348 KB |
| testcase_13 | AC | 4 ms
4,348 KB |
| testcase_14 | AC | 3 ms
4,348 KB |
| testcase_15 | AC | 8 ms
4,348 KB |
| testcase_16 | WA | - |
| testcase_17 | WA | - |
| testcase_18 | WA | - |
| testcase_19 | WA | - |
| testcase_20 | WA | - |
ソースコード
#include <bits/stdc++.h>
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using f64 = double;
using f80 = long double;
using f128 = __float128;
constexpr i32 operator"" _i32(u64 v)
{
return v;
}
constexpr i32 operator"" _u32(u64 v)
{
return v;
}
constexpr i64 operator"" _i64(u64 v)
{
return v;
}
constexpr u64 operator"" _u64(u64 v)
{
return v;
}
constexpr f64 operator"" _f64(f80 v)
{
return v;
}
constexpr f80 operator"" _f80(f80 v)
{
return v;
}
using Istream = std::istream;
using Ostream = std::ostream;
using Str = std::string;
template<typename T>
using Lt = std::less<T>;
template<typename T>
using Gt = std::greater<T>;
template<typename T>
using IList = std::initializer_list<T>;
template<int n>
using BSet = std::bitset<n>;
template<typename T1, typename T2>
using Pair = std::pair<T1, T2>;
template<typename... Ts>
using Tup = std::tuple<Ts...>;
template<typename T, int N>
using Arr = std::array<T, N>;
template<typename... Ts>
using Deq = std::deque<Ts...>;
template<typename... Ts>
using Set = std::set<Ts...>;
template<typename... Ts>
using MSet = std::multiset<Ts...>;
template<typename... Ts>
using USet = std::unordered_set<Ts...>;
template<typename... Ts>
using UMSet = std::unordered_multiset<Ts...>;
template<typename... Ts>
using Map = std::map<Ts...>;
template<typename... Ts>
using MMap = std::multimap<Ts...>;
template<typename... Ts>
using UMap = std::unordered_map<Ts...>;
template<typename... Ts>
using UMMap = std::unordered_multimap<Ts...>;
template<typename... Ts>
using Vec = std::vector<Ts...>;
template<typename... Ts>
using Stack = std::stack<Ts...>;
template<typename... Ts>
using Queue = std::queue<Ts...>;
template<typename T>
using MaxHeap = std::priority_queue<T>;
template<typename T>
using MinHeap = std::priority_queue<T, Vec<T>, Gt<T>>;
using NSec = std::chrono::nanoseconds;
using USec = std::chrono::microseconds;
using MSec = std::chrono::milliseconds;
using Sec = std::chrono::seconds;
template<typename T>
constexpr T LIMMIN = std::numeric_limits<T>::min();
template<typename T>
constexpr T LIMMAX = std::numeric_limits<T>::max();
template<typename T>
constexpr T INF = (LIMMAX<T> - 1) / 2;
template<typename T>
constexpr T PI = T{3.141592653589793238462643383279502884};
template<typename T = u64>
constexpr T TEN(const int n)
{
return n == 0 ? T{1} : TEN<T>(n - 1) * T{10};
}
Ostream& operator<<(Ostream& os, i128 v)
{
bool minus = false;
if (v < 0) { minus = true, v = -v; }
Str ans;
if (v == 0) { ans = "0"; }
while (v) {
ans.push_back('0' + v % 10), v /= 10;
}
std::reverse(ans.begin(), ans.end());
return os << (minus ? "-" : "") << ans;
}
Ostream& operator<<(Ostream& os, u128 v)
{
Str ans;
if (v == 0) { ans = "0"; }
while (v) {
ans.push_back('0' + v % 10), v /= 10;
}
std::reverse(ans.begin(), ans.end());
return os << ans;
}
template<typename T>
bool chmin(T& a, const T& b)
{
if (a > b) {
a = b;
return true;
} else {
return false;
}
}
template<typename T>
bool chmax(T& a, const T& b)
{
if (a < b) {
a = b;
return true;
} else {
return false;
}
}
template<typename T>
constexpr T floorDiv(T x, T y)
{
if (y < T{}) { x = -x, y = -y; }
return x >= T{} ? x / y : (x - y + 1) / y;
}
template<typename T>
constexpr T ceilDiv(T x, T y)
{
if (y < T{}) { x = -x, y = -y; }
return x >= T{} ? (x + y - 1) / y : x / y;
}
template<typename T, typename I>
constexpr T modPower(T v, I n, T mod)
{
T ans = 1 % mod;
for (; n > 0; n >>= 1, (v *= v) %= mod) {
if (n % 2 == 1) { (ans *= v) %= mod; }
}
return ans;
}
template<typename T, typename I>
constexpr T power(T v, I n)
{
T ans = 1;
for (; n > 0; n >>= 1, v *= v) {
if (n % 2 == 1) { ans *= v; }
}
return ans;
}
template<typename T, typename I>
constexpr T power(T v, I n, const T& e)
{
T ans = e;
for (; n > 0; n >>= 1, v *= v) {
if (n % 2 == 1) { ans *= v; }
}
return ans;
}
template<typename T>
Vec<T>& operator+=(Vec<T>& vs1, const Vec<T>& vs2)
{
vs1.insert(vs1.end(), vs2.begin(), vs2.end());
return vs1;
}
template<typename T>
Vec<T> operator+(const Vec<T>& vs1, const Vec<T>& vs2)
{
auto vs = vs1;
vs += vs2;
return vs;
}
template<typename Vs, typename V>
void fillAll(Vs& arr, const V& v)
{
if constexpr (std::is_convertible<V, Vs>::value) {
arr = v;
} else {
for (auto& subarr : arr) {
fillAll(subarr, v);
}
}
}
template<typename Vs>
void sortAll(Vs& vs)
{
std::sort(std::begin(vs), std::end(vs));
}
template<typename Vs, typename C>
void sortAll(Vs& vs, C comp)
{
std::sort(std::begin(vs), std::end(vs), comp);
}
template<typename Vs>
void reverseAll(Vs& vs)
{
std::reverse(std::begin(vs), std::end(vs));
}
template<typename V, typename Vs>
V sumAll(const Vs& vs)
{
if constexpr (std::is_convertible<Vs, V>::value) {
return static_cast<V>(vs);
} else {
V ans = 0;
for (const auto& v : vs) {
ans += sumAll<V>(v);
}
return ans;
}
}
template<typename Vs>
int minInd(const Vs& vs)
{
return std::min_element(std::begin(vs), std::end(vs)) - std::begin(vs);
}
template<typename Vs>
int maxInd(const Vs& vs)
{
return std::max_element(std::begin(vs), std::end(vs)) - std::begin(vs);
}
template<typename Vs, typename V>
int lbInd(const Vs& vs, const V& v)
{
return std::lower_bound(std::begin(vs), std::end(vs), v) - std::begin(vs);
}
template<typename Vs, typename V>
int ubInd(const Vs& vs, const V& v)
{
return std::upper_bound(std::begin(vs), std::end(vs), v) - std::begin(vs);
}
template<typename Vs, typename V>
bool contains(const Vs& vs, const V& v)
{
const int li = lbInd(vs, v);
return (li < std::size(vs) and vs[li] == v);
}
template<typename Vs, typename V>
void plusAll(Vs& vs, const V& v)
{
for (auto& v_ : vs) {
v_ += v;
}
}
template<typename T, typename F>
Vec<T> genVec(int n, F gen)
{
Vec<T> ans;
std::generate_n(std::back_insert_iterator(ans), n, gen);
return ans;
}
template<typename T = int>
Vec<T> iotaVec(int n, T offset = 0)
{
Vec<T> ans(n);
std::iota(ans.begin(), ans.end(), offset);
return ans;
}
constexpr int popcount(const u64 v)
{
return v ? __builtin_popcountll(v) : 0;
}
constexpr int log2p1(const u64 v)
{
return v ? 64 - __builtin_clzll(v) : 0;
}
constexpr int lsbp1(const u64 v)
{
return __builtin_ffsll(v);
}
constexpr int clog(const u64 v)
{
return v ? log2p1(v - 1) : 0;
}
constexpr u64 ceil2(const u64 v)
{
const int l = clog(v);
return (l == 64) ? 0_u64 : (1_u64 << l);
}
constexpr u64 floor2(const u64 v)
{
return v ? (1_u64 << (log2p1(v) - 1)) : 0_u64;
}
constexpr bool ispow2(const u64 v)
{
return (v > 0) and ((v & (v - 1)) == 0);
}
constexpr bool btest(const u64 mask, const int ind)
{
return (mask >> ind) & 1_u64;
}
template<typename F>
struct Fix : F
{
Fix(F&& f) : F{std::forward<F>(f)} {}
template<typename... Args>
auto operator()(Args&&... args) const
{
return F::operator()(*this, std::forward<Args>(args)...);
}
};
class irange
{
private:
struct itr
{
itr(i64 start = 0, i64 step = 1) : m_cnt{start}, m_step{step} {}
bool operator!=(const itr& it) const
{
return m_cnt != it.m_cnt;
}
int operator*()
{
return m_cnt;
}
itr& operator++()
{
m_cnt += m_step;
return *this;
}
i64 m_cnt, m_step;
};
i64 m_start, m_end, m_step;
public:
irange(i64 start, i64 end, i64 step = 1)
{
assert(step != 0);
const i64 d = std::abs(step);
const i64 l = (step > 0 ? start : end);
const i64 r = (step > 0 ? end : start);
int n = (r - l) / d + ((r - l) % d ? 1 : 0);
if (l >= r) { n = 0; }
m_start = start;
m_end = start + step * n;
m_step = step;
}
itr begin() const
{
return itr{m_start, m_step};
}
itr end() const
{
return itr{m_end, m_step};
}
};
irange rep(i64 end)
{
return irange(0, end, 1);
}
irange per(i64 rend)
{
return irange(rend - 1, -1, -1);
}
/**
* @ref https://prng.di.unimi.it
*/
namespace xoshiro_impl {
u64 x;
u64 next()
{
uint64_t z = (x += 0x9e3779b97f4a7c15);
z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
return z ^ (z >> 31);
}
} // namespace xoshiro_impl
class Xoshiro32
{
public:
using result_type = u32;
using T = result_type;
Xoshiro32(T seed = 0)
{
xoshiro_impl::x = seed;
s[0] = xoshiro_impl::next();
s[1] = xoshiro_impl::next();
s[2] = xoshiro_impl::next();
s[3] = xoshiro_impl::next();
}
static constexpr T min()
{
return LIMMIN<T>;
}
static constexpr T max()
{
return LIMMAX<T>;
}
T operator()()
{
return next();
}
private:
static constexpr T rotl(const T x, int k)
{
return (x << k) | (x >> (32 - k));
}
T next()
{
const T ans = rotl(s[1] * 5, 7) * 9;
const T t = s[1] << 9;
s[2] ^= s[0];
s[3] ^= s[1];
s[1] ^= s[2];
s[0] ^= s[3];
s[2] ^= t;
s[3] = rotl(s[3], 11);
return ans;
}
T s[4];
};
class Xoshiro64
{
public:
using result_type = u64;
using T = result_type;
Xoshiro64(T seed = 0)
{
xoshiro_impl::x = seed;
s[0] = xoshiro_impl::next();
s[1] = xoshiro_impl::next();
s[2] = xoshiro_impl::next();
s[3] = xoshiro_impl::next();
}
static constexpr T min()
{
return LIMMIN<T>;
}
static constexpr T max()
{
return LIMMAX<T>;
}
T operator()()
{
return next();
}
private:
static constexpr T rotl(const T x, int k)
{
return (x << k) | (x >> (64 - k));
}
T next()
{
const T ans = rotl(s[1] * 5, 7) * 9;
const T t = s[1] << 17;
s[2] ^= s[0];
s[3] ^= s[1];
s[1] ^= s[2];
s[0] ^= s[3];
s[2] ^= t;
s[3] = rotl(s[3], 45);
return ans;
}
T s[4];
};
template<typename Rng>
class RNG
{
public:
using result_type = typename Rng::result_type;
using T = result_type;
static constexpr T min()
{
return Rng::min();
}
static constexpr T max()
{
return Rng::max();
}
RNG() : RNG(std::random_device{}()) {}
RNG(T seed) : m_rng(seed) {}
T operator()()
{
return m_rng();
}
template<typename T>
T val(T min, T max)
{
return std::uniform_int_distribution<T>(min, max)(m_rng);
}
template<typename T>
Pair<T, T> pair(T min, T max)
{
return std::minmax({val<T>(min, max), val<T>(min, max)});
}
template<typename T>
Vec<T> vec(int n, T min, T max)
{
return genVec<T>(n, [&]() { return val<T>(min, max); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m, T min, T max)
{
return genVec<Vec<T>>(n, [&]() { return vec(m, min, max); });
}
private:
Rng m_rng;
};
RNG<std::mt19937> rng;
RNG<std::mt19937_64> rng64;
RNG<Xoshiro32> rng_xo;
RNG<Xoshiro64> rng_xo64;
class Scanner
{
public:
Scanner(Istream& is = std::cin) : m_is{is}
{
m_is.tie(nullptr)->sync_with_stdio(false);
}
template<typename T>
T val()
{
T v;
return m_is >> v, v;
}
template<typename T>
T val(T offset)
{
return val<T>() - offset;
}
template<typename T>
Vec<T> vec(int n)
{
return genVec<T>(n, [&]() { return val<T>(); });
}
template<typename T>
Vec<T> vec(int n, T offset)
{
return genVec<T>(n, [&]() { return val<T>(offset); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m)
{
return genVec<Vec<T>>(n, [&]() { return vec<T>(m); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m, const T offset)
{
return genVec<Vec<T>>(n, [&]() { return vec<T>(m, offset); });
}
template<typename... Args>
auto tup()
{
return Tup<Args...>{val<Args>()...};
}
template<typename... Args>
auto tup(const Args&... offsets)
{
return Tup<Args...>{val<Args>(offsets)...};
}
private:
Istream& m_is;
};
Scanner in;
class Printer
{
public:
Printer(Ostream& os = std::cout) : m_os{os}
{
m_os << std::fixed << std::setprecision(15);
}
template<typename... Args>
int operator()(const Args&... args)
{
dump(args...);
return 0;
}
template<typename... Args>
int ln(const Args&... args)
{
dump(args...), m_os << '\n';
return 0;
}
template<typename... Args>
int el(const Args&... args)
{
dump(args...), m_os << std::endl;
return 0;
}
private:
template<typename T>
void dump(const T& v)
{
m_os << v;
}
template<typename T>
void dump(const Vec<T>& vs)
{
for (const int i : rep(vs.size())) {
m_os << (i ? " " : ""), dump(vs[i]);
}
}
template<typename T>
void dump(const Vec<Vec<T>>& vss)
{
for (const int i : rep(vss.size())) {
m_os << (i ? "\n" : ""), dump(vss[i]);
}
}
template<typename T, typename... Ts>
int dump(const T& v, const Ts&... args)
{
dump(v), m_os << ' ', dump(args...);
return 0;
}
Ostream& m_os;
};
Printer out;
template<u32 mod_, u32 root_, u32 max2p_>
class modint
{
template<typename U = u32&>
static U modRef()
{
static u32 s_mod = 0;
return s_mod;
}
template<typename U = u32&>
static U rootRef()
{
static u32 s_root = 0;
return s_root;
}
template<typename U = u32&>
static U max2pRef()
{
static u32 s_max2p = 0;
return s_max2p;
}
public:
static constexpr bool isDynamic()
{
return (mod_ == 0);
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> mod()
{
return mod_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> mod()
{
return modRef();
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> root()
{
return root_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> root()
{
return rootRef();
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> max2p()
{
return max2p_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> max2p()
{
return max2pRef();
}
template<typename U = u32>
static void setMod(std::enable_if_t<mod_ == 0, U> m)
{
modRef() = m;
}
template<typename U = u32>
static void setRoot(std::enable_if_t<mod_ == 0, U> r)
{
rootRef() = r;
}
template<typename U = u32>
static void setMax2p(std::enable_if_t<mod_ == 0, U> m)
{
max2pRef() = m;
}
constexpr modint() : m_val{0} {}
constexpr modint(i64 v) : m_val{normll(v)} {}
constexpr void setRaw(u32 v)
{
m_val = v;
}
constexpr modint operator-() const
{
return modint{0} - (*this);
}
constexpr modint& operator+=(const modint& m)
{
m_val = norm(m_val + m.val());
return *this;
}
constexpr modint& operator-=(const modint& m)
{
m_val = norm(m_val + mod() - m.val());
return *this;
}
constexpr modint& operator*=(const modint& m)
{
m_val = normll((i64)m_val * (i64)m.val() % (i64)mod());
return *this;
}
constexpr modint& operator/=(const modint& m)
{
return *this *= m.inv();
}
constexpr modint operator+(const modint& m) const
{
auto v = *this;
return v += m;
}
constexpr modint operator-(const modint& m) const
{
auto v = *this;
return v -= m;
}
constexpr modint operator*(const modint& m) const
{
auto v = *this;
return v *= m;
}
constexpr modint operator/(const modint& m) const
{
auto v = *this;
return v /= m;
}
constexpr bool operator==(const modint& m) const
{
return m_val == m.val();
}
constexpr bool operator!=(const modint& m) const
{
return not(*this == m);
}
friend Istream& operator>>(Istream& is, modint& m)
{
i64 v;
return is >> v, m = v, is;
}
friend Ostream& operator<<(Ostream& os, const modint& m)
{
return os << m.val();
}
constexpr u32 val() const
{
return m_val;
}
template<typename I>
constexpr modint pow(I n) const
{
return power(*this, n);
}
constexpr modint inv() const
{
return pow(mod() - 2);
}
static modint sinv(u32 n)
{
static Vec<modint> is{1, 1};
for (u32 i = (u32)is.size(); i <= n; i++) {
is.push_back(-is[mod() % i] * (mod() / i));
}
return is[n];
}
static modint fact(u32 n)
{
static Vec<modint> fs{1, 1};
for (u32 i = (u32)fs.size(); i <= n; i++) {
fs.push_back(fs.back() * i);
}
return fs[n];
}
static modint ifact(u32 n)
{
static Vec<modint> ifs{1, 1};
for (u32 i = (u32)ifs.size(); i <= n; i++) {
ifs.push_back(ifs.back() * sinv(i));
}
return ifs[n];
}
static modint comb(int n, int k)
{
return k > n or k < 0 ? modint{0} : fact(n) * ifact(n - k) * ifact(k);
}
private:
static constexpr u32 norm(u32 x)
{
return x < mod() ? x : x - mod();
}
static constexpr u32 normll(i64 x)
{
return norm(u32(x % (i64)mod() + (i64)mod()));
}
u32 m_val;
};
using modint_1000000007 = modint<1000000007, 5, 1>;
using modint_998244353 = modint<998244353, 3, 23>;
template<int id>
using modint_dynamic = modint<0, 0, id>;
template<typename mint>
class NTT
{
// DynamicModint 非対応
public:
static Vec<mint> convolute(Vec<mint> as, Vec<mint> bs)
{
const int AN = as.size();
const int BN = bs.size();
const int CN = AN + BN - 1;
const int L = clog(CN);
const int N = (1 << L);
as.resize(N, 0), bs.resize(N, 0);
transform(as, L, false), transform(bs, L, false);
for (int i : rep(N)) {
as[i] *= bs[i];
}
transform(as, L, true);
as.resize(CN);
return as;
}
static void transform(Vec<mint>& as, int L, bool rev)
{
const int N = as.size();
const int N_MAX = 1 << mint::max2p();
assert(N <= N_MAX);
assert((1 << L) == N);
if (N == 1) { return; }
const auto l_range = (rev ? irange(1, L + 1, 1) : irange(L, 0, -1));
for (int l : l_range) {
const int H = 1 << l;
const int B = N / H;
for (int b : rep(B)) {
const mint W = zeta(l, rev);
mint W_h = 1;
for (int h : rep(H / 2)) {
const int y1 = H * b + h;
const int y2 = y1 + H / 2;
const mint a1 = as[y1];
const mint a2 = as[y2];
const mint na1 = (rev ? a1 + a2 * W_h : a1 + a2);
const mint na2 = (rev ? a1 - a2 * W_h : (a1 - a2) * W_h);
as[y1] = na1;
as[y2] = na2;
W_h *= W;
}
}
}
if (rev) {
const mint iN = mint::sinv(N);
for (auto& a : as) {
a *= iN;
}
}
}
private:
static mint zeta(int i, bool rev)
{
static Vec<mint> zs; // zs[i] = 1の2^i乗根
static Vec<mint> izs; // izs[i] = zs[i]の逆元
if (zs.empty()) {
const int MOD = mint::mod();
const int L_MAX = mint::max2p();
const u32 ROOT = mint::root();
zs.resize(L_MAX + 1, 1);
izs.resize(L_MAX + 1, 1);
zs[L_MAX] = mint().pow((MOD - 1) / (1 << L_MAX));
izs[L_MAX] = zs[L_MAX].inv();
for (int l : per(L_MAX)) {
zs[l] = zs[l + 1] * zs[l + 1];
izs[l] = izs[l + 1] * izs[l + 1];
}
}
return (rev ? izs[i] : zs[i]);
}
};
class Garner
{
public:
template<typename mint, typename mint1, typename mint2>
static mint restore_mod(const mint1& x1, const mint2& x2)
{
constexpr auto m1 = mint1::mod();
const auto [y0, y1] = coeff(x1, x2);
return mint(y0.val()) + mint(y1.val()) * m1;
}
template<typename mint, typename mint1, typename mint2, typename mint3>
static mint restore_mod(const mint1& x1, const mint2& x2, const mint3& x3)
{
constexpr auto m1 = mint1::mod();
constexpr auto m2 = mint2::mod();
const auto [y0, y1, y2] = coeff(x1, x2, x3);
return mint(y0.val()) + mint(y1.val()) * m1 + mint(y2.val()) * m1 * m2;
}
template<typename mint1, typename mint2>
static i64 restore_i64(const mint1& x1, const mint2& x2)
{
constexpr u32 m1 = mint1::mod();
constexpr u32 m2 = mint2::mod();
const auto [y0, y1] = coeff(x1, x2);
constexpr u64 MAX = 1_u64 << 63;
const i128 M = (i128)m1 * m2;
i128 S = i128(y0.val()) + i128(y1.val()) * m1;
if (S >= MAX) { S -= M; }
return (i64)S;
}
template<typename mint1, typename mint2, typename mint3>
static i64 restore_i64(const mint1& x1, const mint2& x2, const mint3& x3)
{
constexpr u32 m1 = mint1::mod();
constexpr u32 m2 = mint2::mod();
constexpr u32 m3 = mint3::mod();
const auto [y0, y1, y2] = coeff(x1, x2, x3);
constexpr u64 MAX = 1_u64 << 63;
const i128 M = (i128)m1 * m2 * m3;
i128 S
= i128(y0.val()) + i128(y1.val()) * m1 + i128(y2.val()) * m1 * m2;
if (S >= MAX) { S -= M; }
return (i64)S;
}
private:
template<typename mint1, typename mint2>
static Pair<mint1, mint2> coeff(const mint1& x1, const mint2& x2)
{
constexpr auto m1 = mint1::mod();
constexpr mint2 m1_inv = mint2(m1).inv();
const mint1 y0 = x1;
const mint2 y1 = (x2 - mint2(y0.val())) * m1_inv;
return {y0, y1};
}
template<typename mint1, typename mint2, typename mint3>
static Tup<mint1, mint2, mint3>
coeff(const mint1& x1, const mint2& x2, const mint3& x3)
{
constexpr auto m1 = mint1::mod();
constexpr auto m2 = mint2::mod();
constexpr mint2 m1_inv = mint2(m1).inv();
constexpr mint3 m1m2_inv = (mint3(m1) * mint3(m2)).inv();
const mint1 y0 = x1;
const mint2 y1 = (x2 - mint2(y0.val())) * m1_inv;
const mint3 y2
= (x3 - mint3(y0.val()) - mint3(y1.val()) * m1) * m1m2_inv;
return {y0, y1, y2};
}
};
template<typename mint>
Vec<mint> convolute_mod(const Vec<mint>& as, const Vec<mint>& bs)
{
const u32 L_MAX = mint::max2p();
const u32 N_MAX = (1 << L_MAX);
const int AN = as.size();
const int BN = bs.size();
const int N = AN + BN - 1;
if (N <= 10) {
Vec<mint> cs(N, 0);
for (int i : rep(AN)) {
for (int j : rep(BN)) {
cs[i + j] += as[i] * bs[j];
}
}
return cs;
}
if (N <= N_MAX) {
// mintはNTT Friendlyなのでそのまま畳み込み
return NTT<mint>::convolute(as, bs);
} else {
assert(N <= (1 << 24));
using submint1 = modint<469762049, 3, 26>;
using submint2 = modint<167772161, 3, 25>;
using submint3 = modint<754974721, 11, 24>;
// mod 3つでGarner復元
Vec<submint1> as1(AN), bs1(BN);
Vec<submint2> as2(AN), bs2(BN);
Vec<submint3> as3(AN), bs3(BN);
for (int i : rep(AN)) {
as1[i] = as[i].val(), as2[i] = as[i].val(), as3[i] = as[i].val();
}
for (int i : rep(BN)) {
bs1[i] = bs[i].val(), bs2[i] = bs[i].val(), bs3[i] = bs[i].val();
}
const auto cs1 = NTT<submint1>::convolute(as1, bs1);
const auto cs2 = NTT<submint2>::convolute(as2, bs2);
const auto cs3 = NTT<submint3>::convolute(as3, bs3);
Vec<mint> cs(N);
for (int i : rep(N)) {
cs[i] = Garner::restore_mod<mint>(cs1[i], cs2[i], cs3[i]);
}
return cs;
}
}
template<typename I>
Vec<i64> convolute_i64(const Vec<I>& as, const Vec<I>& bs)
{
const int AN = as.size();
const int BN = bs.size();
const int N = AN + BN - 1;
assert(N <= (1 << 24));
if (N <= 10) {
Vec<i64> cs(N, 0);
for (int i : rep(AN)) {
for (int j : rep(BN)) {
cs[i + j] += (i64)as[i] * bs[j];
}
}
return cs;
}
using submint1 = modint<469762049, 3, 26>;
using submint2 = modint<167772161, 3, 25>;
using submint3 = modint<754974721, 11, 24>;
// mod 3つでGarner復元
Vec<submint1> as1(AN), bs1(BN);
Vec<submint2> as2(AN), bs2(BN);
Vec<submint3> as3(AN), bs3(BN);
for (int i : rep(AN)) {
as1[i] = as[i], as2[i] = as[i], as3[i] = as[i];
}
for (int i : rep(BN)) {
bs1[i] = bs[i], bs2[i] = bs[i], bs3[i] = bs[i];
}
const auto cs1 = NTT<submint1>::convolute(as1, bs1);
const auto cs2 = NTT<submint2>::convolute(as2, bs2);
const auto cs3 = NTT<submint3>::convolute(as3, bs3);
Vec<i64> cs(N);
for (int i : rep(N)) {
cs[i] = Garner::restore_i64(cs1[i], cs2[i], cs3[i]);
}
return cs;
}
int main()
{
using mint = modint_dynamic<0>;
// auto convolute = [&](const Vec<mint>& as, const Vec<mint>& bs) {
// Vec<mint> cs(as.size() + bs.size() - 1, 0);
// cs.shrink_to_fit();
// for (int a : rep(as.size())) {
// for (int b : rep(bs.size())) {
// cs[a + b] += as[a] * bs[b];
// }
// }
// return cs;
// };
auto [N, M, C] = in.tup<int, u32, int>();
mint::setMod(M);
bool complement = false;
if (N - C < C) {
C = N - C;
complement = true;
}
auto As = in.vec<int>(N);
As.shrink_to_fit();
const int A = sumAll<int>(As);
sortAll(As, Gt<int>{});
i64 MAX = 0;
int L = 0;
for (int i : rep(N)) {
if (chmax(MAX, (i64)As[i] * (i + 1))) { L = i + 1; }
}
const int R = N - L;
void(0);
Vec<int> Bs, Cs;
for (int i : rep(N)) {
if (i < L) {
Bs.push_back(As[i]);
} else {
Cs.push_back(As[i]);
}
}
Bs.shrink_to_fit();
Cs.shrink_to_fit();
const int OFFSET = Bs.back();
void(0);
const int BN = std::min(C, L);
Vec<Vec<mint>> bdps(BN + 1);
bdps.shrink_to_fit();
bdps[0] = {1};
bdps[0].shrink_to_fit();
for (int i : rep(L)) {
for (int c : per(std::min(i + 1, BN))) {
for (int j : per(bdps[c].size())) {
const int nj = j + Bs[i] - OFFSET;
if (bdps[c + 1].size() < nj + 1) {
bdps[c + 1].resize(nj + 1);
bdps[c + 1].shrink_to_fit();
}
bdps[c + 1][nj] += bdps[c][j];
}
}
}
// SHOW(bdps);
const int CN = std::min(C, R);
Vec<Vec<mint>> cdps(CN + 1);
cdps.shrink_to_fit();
cdps[0] = {1};
cdps[0].shrink_to_fit();
for (int i : rep(R)) {
for (int c : per(std::min(i + 1, CN))) {
for (int j : per(cdps[c].size())) {
const int nj = j + Cs[i];
if (cdps[c + 1].size() < nj + 1) {
cdps[c + 1].resize(nj + 1);
cdps[c + 1].shrink_to_fit();
}
cdps[c + 1][nj] += cdps[c][j];
}
}
}
// SHOW(cdps);
Vec<mint> ans(A);
for (int c : rep(BN + 1)) {
const int d = C - c;
if (d < 0) { break; }
if (d > CN) { continue; }
auto dp = convolute_mod(bdps[c], cdps[d]);
dp.shrink_to_fit();
for (int i : rep(dp.size())) {
const int a_ = i + OFFSET * c;
const int a = (complement ? A - a_ : a_);
if (a > 0) { ans[a - 1] += dp[i]; }
}
}
out.ln(ans);
int Mem = 0;
for (int i : rep(BN + 1)) {
Mem += bdps[i].size();
}
for (int i : rep(CN + 1)) {
Mem += cdps[i].size();
}
void(0);
return 0;
}