結果
| 問題 | No.1783 Remix Sum |
| ユーザー |
 yosupot
|
| 提出日時 | 2021-12-14 07:30:00 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 65,205 bytes |
| コンパイル時間 | 5,248 ms |
| コンパイル使用メモリ | 281,044 KB |
| 実行使用メモリ | 5,804 KB |
| 最終ジャッジ日時 | 2023-09-30 14:40:11 |
| 合計ジャッジ時間 | 49,496 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge13 |
（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
4,376 KB |
| testcase_01 | AC | 2 ms
4,376 KB |
| testcase_02 | AC | 1 ms
4,384 KB |
| testcase_03 | AC | 2 ms
4,380 KB |
| testcase_04 | AC | 101 ms
4,376 KB |
| testcase_05 | AC | 100 ms
4,380 KB |
| testcase_06 | AC | 522 ms
4,380 KB |
| testcase_07 | AC | 8,585 ms
5,768 KB |
| testcase_08 | AC | 1,257 ms
4,376 KB |
| testcase_09 | AC | 1,259 ms
4,380 KB |
| testcase_10 | AC | 100 ms
4,380 KB |
| testcase_11 | AC | 100 ms
4,376 KB |
| testcase_12 | AC | 8,576 ms
5,804 KB |
| testcase_13 | AC | 8,582 ms
5,800 KB |
| testcase_14 | AC | 1,252 ms
4,376 KB |
| testcase_15 | TLE | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
| testcase_39 | -- | - |
| testcase_40 | -- | - |
| testcase_41 | -- | - |
| testcase_42 | -- | - |
| testcase_43 | -- | - |
| testcase_44 | -- | - |
| testcase_45 | -- | - |
| testcase_46 | -- | - |
| testcase_47 | -- | - |
| testcase_48 | -- | - |
| testcase_49 | -- | - |
| testcase_50 | -- | - |
| testcase_51 | -- | - |
| testcase_52 | -- | - |
| testcase_53 | -- | - |
| testcase_54 | -- | - |
| testcase_55 | -- | - |
| testcase_56 | -- | - |
| testcase_57 | -- | - |
| testcase_58 | -- | - |
| testcase_59 | -- | - |
| testcase_60 | -- | - |
| testcase_61 | -- | - |
| testcase_62 | -- | - |
| testcase_63 | -- | - |
| testcase_64 | -- | - |
| testcase_65 | -- | - |
| testcase_66 | -- | - |
| testcase_67 | -- | - |
| testcase_68 | -- | - |
| testcase_69 | -- | - |
| testcase_70 | -- | - |
| testcase_71 | -- | - |
| testcase_72 | -- | - |
| testcase_73 | -- | - |
| testcase_74 | -- | - |
| testcase_75 | -- | - |
| testcase_76 | -- | - |
| testcase_77 | -- | - |
| testcase_78 | -- | - |
| testcase_79 | -- | - |
ソースコード
//#pragma GCC optimize("Ofast")
#pragma GCC target("avx2")
//#undef LOCAL
#include <algorithm>
#include <array>
#include <cassert>
#include <type_traits>
#include <vector>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
template <class mint,
int g = internal::primitive_root<mint::mod()>,
internal::is_static_modint_t<mint>* = nullptr>
struct fft_info {
static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1
std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1
std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;
std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;
fft_info() {
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
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];
}
}
}
};
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::ceil_pow2(n);
static const fft_info<mint> info;
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 (int s = 0; s < (1 << len); s++) {
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
if (s + 1 != (1 << len))
rot *= info.rate2[bsf(~(unsigned int)(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::mod() * mint::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);
}
if (s + 1 != (1 << len))
rot *= info.rate3[bsf(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::ceil_pow2(n);
static const fft_info<mint> info;
int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
for (int s = 0; s < (1 << (len - 1)); s++) {
int offset = s << (h - len + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
irot.val();
;
}
if (s + 1 != (1 << (len - 1)))
irot *= info.irate2[bsf(~(unsigned int)(s))];
}
len--;
} else {
int p = 1 << (h - len);
mint irot = 1, iimag = info.iroot[2];
for (int s = 0; s < (1 << (len - 2)); s++) {
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::mod() + a2 - a3) * iimag.val()).val();
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] =
(a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
a[i + offset + 2 * p] =
(a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
irot2.val();
a[i + offset + 3 * p] =
(a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
irot3.val();
}
if (s + 1 != (1 << (len - 2)))
irot *= info.irate3[bsf(~(unsigned int)(s))];
}
len -= 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint>& a,
const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
std::vector<mint> ans(n + m - 1);
if (n < m) {
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) {
ans[i + j] += a[i] * b[j];
}
}
} else {
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
}
return ans;
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(const std::vector<mint>& a,
const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
const std::vector<long long>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
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 constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
long long diff =
c1[i] - internal::safe_mod((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;
}
} // namespace atcoder
#include <unistd.h>
#include <algorithm>
#include <array>
#include <cassert>
#include <cctype>
#include <cstring>
#include <sstream>
#include <string>
#include <type_traits>
#include <vector>
namespace yosupo {
namespace internal {
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
} // namespace internal
int bsf(unsigned int n) { return __builtin_ctz(n); }
int bsf(unsigned long n) { return __builtin_ctzl(n); }
int bsf(unsigned long long n) { return __builtin_ctzll(n); }
int bsf(unsigned __int128 n) {
unsigned long long low = (unsigned long long)(n);
unsigned long long high = (unsigned long long)(n >> 64);
return low ? __builtin_ctzll(low) : 64 + __builtin_ctzll(high);
}
int bsr(unsigned int n) {
return 8 * (int)sizeof(unsigned int) - 1 - __builtin_clz(n);
}
int bsr(unsigned long n) {
return 8 * (int)sizeof(unsigned long) - 1 - __builtin_clzl(n);
}
int bsr(unsigned long long n) {
return 8 * (int)sizeof(unsigned long long) - 1 - __builtin_clzll(n);
}
int bsr(unsigned __int128 n) {
unsigned long long low = (unsigned long long)(n);
unsigned long long high = (unsigned long long)(n >> 64);
return high ? 127 - __builtin_clzll(high) : 63 - __builtin_ctzll(low);
}
int popcnt(unsigned int n) { return __builtin_popcount(n); }
int popcnt(unsigned long n) { return __builtin_popcountl(n); }
int popcnt(unsigned long long n) { return __builtin_popcountll(n); }
} // namespace yosupo
#include <cassert>
#include <numeric>
#include <type_traits>
namespace yosupo {
namespace internal {
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral =
typename std::conditional<std::is_integral<T>::value ||
internal::is_signed_int128<T>::value ||
internal::is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
template <class T>
using is_integral_t = std::enable_if_t<is_integral<T>::value>;
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace yosupo
namespace yosupo {
struct Scanner {
public:
Scanner(const Scanner&) = delete;
Scanner& operator=(const Scanner&) = delete;
Scanner(FILE* fp) : fd(fileno(fp)) { line[0] = 127; }
void read() {}
template <class H, class... T> void read(H& h, T&... t) {
bool f = read_single(h);
assert(f);
read(t...);
}
int read_unsafe() { return 0; }
template <class H, class... T> int read_unsafe(H& h, T&... t) {
bool f = read_single(h);
if (!f) return 0;
return 1 + read_unsafe(t...);
}
int close() { return ::close(fd); }
private:
static constexpr int SIZE = 1 << 15;
int fd = -1;
std::array<char, SIZE + 1> line;
int st = 0, ed = 0;
bool eof = false;
bool read_single(std::string& ref) {
if (!skip_space()) return false;
ref = "";
while (true) {
char c = top();
if (c <= ' ') break;
ref += c;
st++;
}
return true;
}
bool read_single(double& ref) {
std::string s;
if (!read_single(s)) return false;
ref = std::stod(s);
return true;
}
template <class T,
std::enable_if_t<std::is_same<T, char>::value>* = nullptr>
bool read_single(T& ref) {
if (!skip_space<50>()) return false;
ref = top();
st++;
return true;
}
template <class T,
internal::is_signed_int_t<T>* = nullptr,
std::enable_if_t<!std::is_same<T, char>::value>* = nullptr>
bool read_single(T& sref) {
using U = internal::to_unsigned_t<T>;
if (!skip_space<50>()) return false;
bool neg = false;
if (line[st] == '-') {
neg = true;
st++;
}
U ref = 0;
do {
ref = 10 * ref + (line[st++] & 0x0f);
} while (line[st] >= '0');
sref = neg ? -ref : ref;
return true;
}
template <class U,
internal::is_unsigned_int_t<U>* = nullptr,
std::enable_if_t<!std::is_same<U, char>::value>* = nullptr>
bool read_single(U& ref) {
if (!skip_space<50>()) return false;
ref = 0;
do {
ref = 10 * ref + (line[st++] & 0x0f);
} while (line[st] >= '0');
return true;
}
bool reread() {
if (ed - st >= 50) return true;
if (st > SIZE / 2) {
std::memmove(line.data(), line.data() + st, ed - st);
ed -= st;
st = 0;
}
if (eof) return false;
auto u = ::read(fd, line.data() + ed, SIZE - ed);
if (u == 0) {
eof = true;
line[ed] = '\0';
u = 1;
}
ed += int(u);
line[ed] = char(127);
return true;
}
char top() {
if (st == ed) {
bool f = reread();
assert(f);
}
return line[st];
}
template <int TOKEN_LEN = 0> bool skip_space() {
while (true) {
while (line[st] <= ' ') st++;
if (ed - st > TOKEN_LEN) return true;
if (st > ed) st = ed;
for (auto i = st; i < ed; i++) {
if (line[i] <= ' ') return true;
}
if (!reread()) return false;
}
}
};
struct Printer {
public:
template <char sep = ' ', bool F = false> void write() {}
template <char sep = ' ', bool F = false, class H, class... T>
void write(const H& h, const T&... t) {
if (F) write_single(sep);
write_single(h);
write<true>(t...);
}
template <char sep = ' ', class... T> void writeln(const T&... t) {
write<sep>(t...);
write_single('\n');
}
Printer(FILE* _fp) : fd(fileno(_fp)) {}
~Printer() { flush(); }
int close() {
flush();
return ::close(fd);
}
void flush() {
if (pos) {
auto res = ::write(fd, line.data(), pos);
assert(res != -1);
pos = 0;
}
}
private:
static std::array<std::array<char, 2>, 100> small;
static std::array<unsigned long long, 20> tens;
static constexpr size_t SIZE = 1 << 15;
int fd;
std::array<char, SIZE> line;
size_t pos = 0;
std::stringstream ss;
template <class T,
std::enable_if_t<std::is_same<char, T>::value>* = nullptr>
void write_single(const T& val) {
if (pos == SIZE) flush();
line[pos++] = val;
}
template <class T,
internal::is_signed_int_t<T>* = nullptr,
std::enable_if_t<!std::is_same<char, T>::value>* = nullptr>
void write_single(const T& val) {
using U = internal::to_unsigned_t<T>;
if (val == 0) {
write_single('0');
return;
}
if (pos > SIZE - 50) flush();
U uval = val;
if (val < 0) {
write_single('-');
uval = -uval;
}
write_unsigned(uval);
}
template <class U, internal::is_unsigned_int_t<U>* = nullptr>
void write_single(U uval) {
if (uval == 0) {
write_single('0');
return;
}
if (pos > SIZE - 50) flush();
write_unsigned(uval);
}
template <class U, internal::is_unsigned_int_t<U>* = nullptr>
static int calc_len(U x) {
int i = (bsr(x) * 3 + 3) / 10;
if (x < tens[i])
return i;
else
return i + 1;
}
template <class U,
internal::is_unsigned_int_t<U>* = nullptr,
std::enable_if_t<2 >= sizeof(U)>* = nullptr>
void write_unsigned(U uval) {
size_t len = calc_len(uval);
pos += len;
char* ptr = line.data() + pos;
while (uval >= 100) {
ptr -= 2;
memcpy(ptr, small[uval % 100].data(), 2);
uval /= 100;
}
if (uval >= 10) {
memcpy(ptr - 2, small[uval].data(), 2);
} else {
*(ptr - 1) = char('0' + uval);
}
}
template <class U,
internal::is_unsigned_int_t<U>* = nullptr,
std::enable_if_t<4 == sizeof(U)>* = nullptr>
void write_unsigned(U uval) {
std::array<char, 8> buf;
memcpy(buf.data() + 6, small[uval % 100].data(), 2);
memcpy(buf.data() + 4, small[uval / 100 % 100].data(), 2);
memcpy(buf.data() + 2, small[uval / 10000 % 100].data(), 2);
memcpy(buf.data() + 0, small[uval / 1000000 % 100].data(), 2);
if (uval >= 100000000) {
if (uval >= 1000000000) {
memcpy(line.data() + pos, small[uval / 100000000 % 100].data(),
2);
pos += 2;
} else {
line[pos] = char('0' + uval / 100000000);
pos++;
}
memcpy(line.data() + pos, buf.data(), 8);
pos += 8;
} else {
size_t len = calc_len(uval);
memcpy(line.data() + pos, buf.data() + (8 - len), len);
pos += len;
}
}
template <class U,
internal::is_unsigned_int_t<U>* = nullptr,
std::enable_if_t<8 == sizeof(U)>* = nullptr>
void write_unsigned(U uval) {
size_t len = calc_len(uval);
pos += len;
char* ptr = line.data() + pos;
while (uval >= 100) {
ptr -= 2;
memcpy(ptr, small[uval % 100].data(), 2);
uval /= 100;
}
if (uval >= 10) {
memcpy(ptr - 2, small[uval].data(), 2);
} else {
*(ptr - 1) = char('0' + uval);
}
}
template <
class U,
std::enable_if_t<internal::is_unsigned_int128<U>::value>* = nullptr>
void write_unsigned(U uval) {
static std::array<char, 50> buf;
size_t len = 0;
while (uval > 0) {
buf[len++] = char((uval % 10) + '0');
uval /= 10;
}
std::reverse(buf.begin(), buf.begin() + len);
memcpy(line.data() + pos, buf.data(), len);
pos += len;
}
void write_single(const std::string& s) {
for (char c : s) write_single(c);
}
void write_single(const char* s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) write_single(s[i]);
}
template <class T> void write_single(const std::vector<T>& val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write_single(' ');
write_single(val[i]);
}
}
};
std::array<std::array<char, 2>, 100> Printer::small = [] {
std::array<std::array<char, 2>, 100> table;
for (int i = 0; i <= 99; i++) {
table[i][1] = char('0' + (i % 10));
table[i][0] = char('0' + (i / 10 % 10));
}
return table;
}();
std::array<unsigned long long, 20> Printer::tens = [] {
std::array<unsigned long long, 20> table;
for (int i = 0; i < 20; i++) {
table[i] = 1;
for (int j = 0; j < i; j++) {
table[i] *= 10;
}
}
return table;
}();
} // namespace yosupo
#include <iostream>
namespace atcoder {
template <int MOD>
std::ostream& operator<<(std::ostream& os, const static_modint<MOD>& x) {
return os << x.val();
}
template <int ID>
std::ostream& operator<<(std::ostream& os, const dynamic_modint<ID>& x) {
return os << x.val();
}
} // namespace atcoder
namespace yosupo {
template <int MOD> using static_modint = atcoder::static_modint<MOD>;
template <int ID> using dynamic_modint = atcoder::dynamic_modint<ID>;
using modint998244353 = atcoder::modint998244353;
using modint1000000007 = atcoder::modint1000000007;
using modint = atcoder::modint;
} // namespace yosupo
static_assert(__cplusplus >= 201703L, "C++17 or later");
#include <immintrin.h>
#include <array>
namespace yosupo {
struct llx4 {
public:
llx4() : d() {}
llx4(long long x) : d(_mm256_set1_epi64x(x)) {}
llx4(const __m256i& x) : d(x) {}
llx4(const std::array<long long, 8>& x)
: d(_mm256_loadu_si256((__m256i*)x.data())) {}
llx4(long long x0, long long x1, long long x2, long long x3)
: d(_mm256_set_epi64x(x3, x2, x1, x0)) {}
std::array<long long, 4> to_array() const {
alignas(32) std::array<long long, 4> b;
_mm256_store_si256((__m256i*)b.data(), d);
return b;
}
long long at(int i) const {
alignas(32) std::array<long long, 4> b;
_mm256_store_si256((__m256i*)b.data(), d);
return b[i];
}
void set(int i, long long x) {
alignas(32) std::array<long long, 4> b;
_mm256_store_si256((__m256i*)b.data(), d);
b[i] = x;
d = _mm256_load_si256((__m256i*)b.data());
}
llx4& operator+=(const llx4& rhs) {
d = _mm256_add_epi64(d, rhs.d);
return *this;
}
friend llx4 operator+(const llx4& lhs, const llx4& rhs) {
return llx4(lhs) += rhs;
}
llx4& operator-=(const llx4& rhs) {
d = _mm256_sub_epi64(d, rhs.d);
return *this;
}
friend llx4 operator-(const llx4& lhs, const llx4& rhs) {
return llx4(lhs) -= rhs;
}
__m256i raw() const { return d; }
__m256i d;
};
struct intx8 {
public:
intx8() : d() {}
intx8(int x) : d(_mm256_set1_epi32(x)) {}
intx8(const __m256i& x) : d(x) {}
intx8(const std::array<int, 8>& x)
: d(_mm256_loadu_si256((__m256i*)x.data())) {}
intx8(int x0, int x1, int x2, int x3, int x4, int x5, int x6, int x7)
: d(_mm256_set_epi32(x7, x6, x5, x4, x3, x2, x1, x0)) {}
std::array<int, 8> to_array() const {
alignas(32) std::array<int, 8> b;
_mm256_store_si256((__m256i*)b.data(), d);
return b;
}
int at(int i) const {
alignas(32) std::array<int, 8> b;
_mm256_store_si256((__m256i*)b.data(), d);
return b[i];
}
void set(int i, int x) {
alignas(32) std::array<int, 8> b;
_mm256_store_si256((__m256i*)b.data(), d);
b[i] = x;
d = _mm256_load_si256((__m256i*)b.data());
}
intx8& operator+=(const intx8& rhs) {
d = _mm256_add_epi32(d, rhs.d);
return *this;
}
friend intx8 operator+(const intx8& lhs, const intx8& rhs) {
return intx8(lhs) += rhs;
}
intx8& operator-=(const intx8& rhs) {
d = _mm256_sub_epi32(d, rhs.d);
return *this;
}
friend intx8 operator-(const intx8& lhs, const intx8& rhs) {
return intx8(lhs) -= rhs;
}
std::pair<llx4, llx4> mul(const intx8 rhs) const {
__m256i x0246 = _mm256_mul_epi32(d, rhs.d);
__m256i x1357 = _mm256_mul_epi32(_mm256_shuffle_epi32(d, 0xf5),
_mm256_shuffle_epi32(rhs.d, 0xf5));
return {x0246, x1357};
}
intx8& operator&=(const intx8& rhs) {
d = _mm256_and_si256(d, rhs.d);
return *this;
}
friend intx8 operator&(const intx8& lhs, const intx8& rhs) {
return intx8(lhs) &= rhs;
}
intx8 operator>(const intx8& rhs) const {
return _mm256_cmpgt_epi32(d, rhs.d);
}
intx8 operator<(const intx8& rhs) const { return rhs > *this; }
bool test_all_zero() const { return _mm256_testz_si256(d, d) == 1; }
intx8 sign() const { return *this < intx8(_mm256_setzero_si256()); }
intx8 abs() const { return _mm256_abs_epi32(d); }
std::pair<llx4, llx4> split() const {
return {
llx4(((*this) & intx8(-1, 0, -1, 0, -1, 0, -1, 0)).d),
llx4(_mm256_srli_epi64(d, 32)),
};
}
__m256i raw() const { return d; }
__m256i d;
};
} // namespace yosupo
namespace yosupo {
template <int MOD>
intx8 montgomery_reduction(const llx4& x0246, const llx4& x1357) {
static_assert(MOD > 0 && MOD % 2, "mod must be positive & odd");
static constexpr int nim =
-(int)atcoder::internal::inv_gcd(MOD, 1LL << 32).second;
__m256i km0246 =
_mm256_mul_epu32(_mm256_mul_epu32(x0246.raw(), _mm256_set1_epi32(nim)),
_mm256_set1_epi32(MOD));
__m256i km1357 =
_mm256_mul_epu32(_mm256_mul_epu32(x1357.raw(), _mm256_set1_epi32(nim)),
_mm256_set1_epi32(MOD));
llx4 z0246 = llx4(x0246) + llx4(km0246);
llx4 z1357 = llx4(x1357) + llx4(km1357);
return _mm256_blend_epi32(_mm256_shuffle_epi32(z0246.raw(), 0xf5),
z1357.raw(), 0b10101010);
}
/*
vectorized modint (by montgomery reduction)
*/
template <int MOD> struct modintx8 {
static_assert(MOD % 2, "mod must be positive & odd");
static_assert(1 <= MOD && MOD <= (1 << 30) - 1,
"mod range: [1, (1<<30) - 1]");
using mint = static_modint<MOD>;
static const int B = ((1LL << 32)) % MOD;
static const int iB = atcoder::internal::inv_gcd(B, MOD).second;
intx8 d;
modintx8() : d(0) {}
modintx8(const std::array<mint, 8>& _d) {
d = intx8(_d[0].val(), _d[1].val(), _d[2].val(), _d[3].val(),
_d[4].val(), _d[5].val(), _d[6].val(), _d[7].val());
(*this) *= modintx8(B);
}
modintx8(mint x0,
mint x1,
mint x2,
mint x3,
mint x4,
mint x5,
mint x6,
mint x7)
: d(_mm256_set_epi32(x7.val(),
x6.val(),
x5.val(),
x4.val(),
x3.val(),
x2.val(),
x1.val(),
x0.val())) {
(*this) *= modintx8(B);
}
modintx8(mint x) : d(int((x * B).val())) {}
mint at(int i) const {
return mint(1ULL * d.at(i) * iB);
}
void set(int i, mint x) {
d.set(i, (x * B).val());
}
modintx8& operator+=(const modintx8& rhs) {
d += rhs.d;
d -= intx8(2 * MOD);
d += intx8(2 * MOD) & d.sign();
return *this;
}
modintx8& operator-=(const modintx8& rhs) {
d -= rhs.d;
d += intx8(2 * MOD) & d.sign();
return *this;
}
modintx8& operator*=(const modintx8& rhs) {
auto v = d.mul(rhs.d);
d = montgomery_reduction<mint::mod()>(v.first, v.second);
return *this;
}
friend modintx8 operator+(const modintx8& lhs, const modintx8& rhs) {
return modintx8(lhs) += rhs;
}
friend modintx8 operator-(const modintx8& lhs, const modintx8& rhs) {
return modintx8(lhs) -= rhs;
}
friend modintx8 operator*(const modintx8& lhs, const modintx8& rhs) {
return modintx8(lhs) *= rhs;
}
template <int N> modintx8 neg() const {
modintx8 w;
w.d = (d - intx8(_mm256_blend_epi32(_mm256_setzero_si256(),
_mm256_set1_epi32(2 * MOD), N)))
.abs();
return w;
}
template <int N> modintx8 shuffle() const {
modintx8 x;
x.d.d = _mm256_shuffle_epi32(d.d, N);
return x;
}
template <int N> modintx8 shufflex4() const {
modintx8 x;
x.d.d = _mm256_permute2x128_si256(d.d, d.d, N);
return x;
}
std::array<mint, 8> to_array() const {
auto buf = (*this * modintx8(iB)).d;
buf -= intx8(MOD) & (buf > intx8(MOD - 1));
auto v = buf.to_array();
std::array<mint, 8> x;
for (int i = 0; i < 8; i++) {
x[i] = mint::raw(v[i]);
}
return x;
}
static modintx8 from_raw(const intx8& _d) {
modintx8 x;
x.d = _d;
return x;
}
};
} // namespace yosupo
#include <immintrin.h>
#include <array>
#include <vector>
namespace yosupo {
template <int MOD> struct fft_info {
using mint = static_modint<MOD>;
using mintx8 = modintx8<MOD>;
static constexpr int g = atcoder::internal::primitive_root<MOD>;
static constexpr int rank2 =
atcoder::internal::bsf_constexpr(mint::mod() - 1);
std::array<mint, rank2 + 1> root,
iroot; // root[i]^(2^i) == 1, root[i] * iroot[i] == 1
std::array<mint, std::max(0, rank2 - 1 + 1)> rate2, irate2;
std::array<mintx8, std::max(0, rank2 - 1 + 1)> rate2x;
std::array<mint, std::max(0, rank2 - 2 + 1)> rate3, irate3;
std::array<mint, std::max(0, rank2 - 3 + 1)> rate4, irate4;
std::array<mintx8, std::max(0, rank2 - 3 + 1)> rate4xi,
irate4xi; // rate4xi[i][j] = rate4[i]^j
fft_info() {
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
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];
}
for (int i = 0; i <= rank2 - 2; i++) {
rate2x[i] = mintx8(rate2[i]);
}
}
{
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];
}
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 4; i++) {
rate4[i] = root[i + 4] * prod;
irate4[i] = iroot[i + 4] * iprod;
prod *= iroot[i + 4];
iprod *= root[i + 4];
std::array<mint, 8> buf, ibuf;
for (int j = 0; j < 8; j++) {
buf[j] = rate4[i].pow(j);
ibuf[j] = irate4[i].pow(j);
}
rate4xi[i] = buf;
irate4xi[i] = ibuf;
}
}
}
};
template <int MOD> void butterfly(std::vector<modintx8<MOD>>& _a) {
int n = int(_a.size() * 8);
using mint = static_modint<MOD>;
using mintx8 = modintx8<MOD>;
int h = internal::ceil_pow2(n);
static const fft_info<MOD> info;
const mint imag = info.root[2];
assert(n >= 8 && n % 8 == 0);
int n8 = n / 8;
int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
if (h % 2 == 0) {
int p = n8 / 2;
for (int i = 0; i < p; i++) {
auto l = _a[i];
auto r = _a[i + p];
_a[i] = l + r;
_a[i + p] = l - r;
}
len++;
}
while (len + 5 <= h) {
int p = 1 << (h - len - 5);
mintx8 rotx(1);
auto imagx = mintx8(imag);
imagx.d -= intx8(998244353) & (imagx.d > intx8(998244352));
for (int s = 0; s < (1 << len); s++) {
auto rot2x = rotx * rotx;
auto rot3x = rot2x * rotx;
int offset = s << (h - len - 3);
for (int i = 0; i < p; i++) {
auto a0 = _a[i + offset + 0 * p];
auto a1 = _a[i + offset + 1 * p] * rotx;
auto a2 = _a[i + offset + 2 * p] * rot2x;
auto a3 = _a[i + offset + 3 * p] * rot3x;
_a[i + offset + 0 * p] = (a0 + a2) + (a1 + a3);
_a[i + offset + 1 * p] = (a0 + a2) - (a1 + a3);
_a[i + offset + 2 * p] = (a0 - a2) + (a1 - a3) * imagx;
_a[i + offset + 3 * p] = (a0 - a2) - (a1 - a3) * imagx;
}
rotx *= mintx8(info.rate3[bsf(~(unsigned int)(s))]);
}
len += 2;
}
{
assert(len + 3 == h);
mint e8 = info.root[3];
const mintx8 step1 = mintx8(1, 1, 1, 1, 1, e8, e8 * e8, e8 * e8 * e8);
const mintx8 step2 = mintx8(1, 1, 1, imag, 1, 1, 1, imag);
auto rotxi = mintx8(1);
for (int s = 0; s < n8; s++) {
mintx8 v = _a[s] * rotxi;
v = (v.template neg<0b11110000>() + v.template shufflex4<0b01>()) *
step1;
v = (v.template neg<0b11001100>() +
v.template shuffle<0b01001110>()) *
step2;
v = (v.template neg<0b10101010>() +
v.template shuffle<0b10110001>());
_a[s] = v;
rotxi *= info.rate4xi[bsf(~(unsigned int)(s))];
}
len += 3;
}
}
template <int MOD> void butterfly_inv(std::vector<modintx8<MOD>>& _a) {
int n = int(_a.size() * 8);
using mint = static_modint<MOD>;
using mintx8 = modintx8<MOD>;
int h = internal::ceil_pow2(n);
static const fft_info<MOD> info;
assert(n >= 8 && n % 8 == 0);
const mint iimag = info.iroot[2];
const mintx8 iimagx = iimag;
int n8 = n / 8;
int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
{
mint ie8 = info.iroot[3];
const mintx8 istep1 =
mintx8(1, 1, 1, 1, 1, ie8, ie8 * ie8, ie8 * ie8 * ie8);
const mintx8 istep2 = mintx8(1, 1, 1, iimag, 1, 1, 1, iimag);
auto irotxi = mintx8(1);
for (int s = 0; s < n8; s++) {
auto v = _a[s];
v = (v.template neg<0b10101010>() +
v.template shuffle<0b10110001>()) *
istep2;
v = (v.template neg<0b11001100>() +
v.template shuffle<0b01001110>()) *
istep1;
v = (v.template neg<0b11110000>() + v.template shufflex4<0b01>()) *
irotxi;
_a[s] = v;
irotxi *= info.irate4xi[bsf(~(unsigned int)(s))];
}
len -= 3;
}
while (len >= 2) {
int p = 1 << (h - len - 3);
auto irotx = mintx8(1);
for (int s = 0; s < (1 << (len - 2)); s++) {
auto irot2x = irotx * irotx;
auto irot3x = irot2x * irotx;
int offset = s << (h - len - 1);
for (int i = 0; i < p; i++) {
auto a0 = _a[i + offset + 0 * p];
auto a1 = _a[i + offset + 1 * p];
auto a2 = _a[i + offset + 2 * p];
auto a3 = _a[i + offset + 3 * p];
auto a0a1 = a0 + a1;
auto a0na1 = a0 - a1;
auto a2a3 = a2 + a3;
auto a2na3iimag = (a2 - a3) * iimagx;
_a[i + offset + 0 * p] = a0a1 + a2a3;
_a[i + offset + 1 * p] = (a0na1 + a2na3iimag) * irotx;
_a[i + offset + 2 * p] = (a0a1 - a2a3) * irot2x;
_a[i + offset + 3 * p] = (a0na1 - a2na3iimag) * irot3x;
}
irotx *= info.irate3[bsf(~(unsigned int)(s))];
}
len -= 2;
}
if (len == 1) {
int p = 1 << (h - 4);
for (int i = 0; i < p; i++) {
auto l = _a[i];
auto r = _a[i + p];
_a[i] = l + r;
_a[i + p] = l - r;
}
len--;
}
}
template <int MOD>
std::vector<modintx8<MOD>> convolution(std::vector<modintx8<MOD>> a,
std::vector<modintx8<MOD>> b) {
int n = int(a.size());
int m = int(b.size());
int z = 1 << internal::ceil_pow2(n + m);
a.resize(z);
butterfly(a);
b.resize(z);
butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
butterfly_inv(a);
a.resize(n + m);
modintx8<MOD> iz = static_modint<MOD>(8 * z).inv();
for (int i = 0; i < n + m; i++) a[i] *= iz;
return a;
}
template <int MOD> void butterfly(std::vector<static_modint<MOD>>& a) {
using mint = static_modint<MOD>;
using mintx8 = modintx8<MOD>;
int n = int(a.size());
int n2 = (n + 7) / 8;
std::vector<mintx8> a2(n2);
for (int i = 0; i < n2; i++) {
std::array<mint, 8> v;
for (int j = 0; j < 8 && (i * 8 + j) < n; j++) {
v[j] = a[i * 8 + j];
}
a2[i] = v;
}
butterfly(a2);
for (int i = 0; i < n2; i++) {
auto v = a2[i].to_array();
for (int j = 0; j < 8 && (i * 8 + j) < n; j++) {
a[i * 8 + j] = v[j];
}
}
}
template <int MOD> void butterfly_inv(std::vector<static_modint<MOD>>& a) {
using mint = static_modint<MOD>;
using mintx8 = modintx8<MOD>;
int n = int(a.size());
int n2 = (n + 7) / 8;
std::vector<mintx8> a2(n2);
for (int i = 0; i < n2; i++) {
std::array<mint, 8> v;
for (int j = 0; j < 8 && (i * 8 + j) < n; j++) {
v[j] = a[i * 8 + j];
}
a2[i] = v;
}
butterfly_inv(a2);
for (int i = 0; i < n2; i++) {
auto v = a2[i].to_array();
for (int j = 0; j < 8 && (i * 8 + j) < n; j++) {
a[i * 8 + j] = v[j];
}
}
}
} // namespace yosupo
using namespace yosupo;
const int mod = 120586241;
using mint = static_modint<mod>;
const mint mg = atcoder::internal::primitive_root<mod>;
const mint g10 = mg.pow((mod - 1) / 10);
const mint ig10 = g10.inv();
const int tens[6] = {
1, 10, 100, 1000, 10000, 100000
};
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <complex>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
#ifdef LOCAL
ostream& operator<<(ostream& os, __int128_t x) {
if (x < 0) {
os << "-";
x *= -1;
}
if (x == 0) {
return os << "0";
}
string s;
while (x) {
s += char(x % 10 + '0');
x /= 10;
}
reverse(s.begin(), s.end());
return os << s;
}
ostream& operator<<(ostream& os, __uint128_t x) {
if (x == 0) {
return os << "0";
}
string s;
while (x) {
s += char(x % 10 + '0');
x /= 10;
}
reverse(s.begin(), s.end());
return os << s;
}
template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p);
template <class T> ostream& operator<<(ostream& os, const V<T>& v);
template <class T> ostream& operator<<(ostream& os, const deque<T>& v);
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T> ostream& operator<<(ostream& os, const set<T>& s);
template <class T, class U>
ostream& operator<<(ostream& os, const map<T, U>& m);
template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
return os << "P(" << p.first << ", " << p.second << ")";
}
template <class T> ostream& operator<<(ostream& os, const V<T>& v) {
os << "[";
bool f = false;
for (auto d : v) {
if (f) os << ", ";
f = true;
os << d;
}
return os << "]";
}
template <class T> ostream& operator<<(ostream& os, const deque<T>& v) {
os << "[";
bool f = false;
for (auto d : v) {
if (f) os << ", ";
f = true;
os << d;
}
return os << "]";
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
os << "[";
bool f = false;
for (auto d : a) {
if (f) os << ", ";
f = true;
os << d;
}
return os << "]";
}
template <class T> ostream& operator<<(ostream& os, const set<T>& s) {
os << "{";
bool f = false;
for (auto d : s) {
if (f) os << ", ";
f = true;
os << d;
}
return os << "}";
}
template <class T> ostream& operator<<(ostream& os, const multiset<T>& s) {
os << "{";
bool f = false;
for (auto d : s) {
if (f) os << ", ";
f = true;
os << d;
}
return os << "}";
}
template <class T, class U>
ostream& operator<<(ostream& os, const map<T, U>& s) {
os << "{";
bool f = false;
for (auto p : s) {
if (f) os << ", ";
f = true;
os << p.first << ": " << p.second;
}
return os << "}";
}
struct PrettyOS {
ostream& os;
bool first;
template <class T> auto operator<<(T&& x) {
if (!first) os << ", ";
first = false;
os << x;
return *this;
}
};
template <class... T> void dbg0(T&&... t) {
(PrettyOS{cerr, true} << ... << t);
}
#define dbg(...) \
do { \
cerr << __LINE__ << " : " << #__VA_ARGS__ << " = "; \
dbg0(__VA_ARGS__); \
cerr << endl; \
} while (false);
#else
#define dbg(...)
#endif
Scanner sc = Scanner(stdin);
Printer pr = Printer(stdout);
V<mint> fft10(const V<mint>& a, mint e) {
assert(int(a.size()) == 10);
V<mint> b(10);
mint base = 1;
for (int i = 0; i < 10; i++) {
mint freq = 1;
for (int j = 0; j < 10; j++) {
b[i] += a[j] * freq;
freq *= base;
}
base *= e;
}
return b;
}
V<mint> conv_naive(int k, const V<mint>& a, const V<mint>& b) {
int n = tens[k];
assert(int(a.size()) == n);
assert(int(b.size()) == n);
V<mint> c(n);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
bool ok = true;
for (int h = 0; h < k; h++) {
int x = i / tens[h] % 10;
int y = j / tens[h] % 10;
if (x + y >= 10) {
ok = false;
break;
}
}
if (ok) {
c[i + j] += a[i] * b[j];
}
}
}
return c;
}
V<int> gen_chi(int k) {
auto _chi = [&](int x) {
int sum = 0;
for (int i = 0; i < k - 1; i++) {
sum += x / tens[i + 1];
}
return sum;
};
int N = tens[k];
V<int> chi(N);
for (int i = 0; i < N; i++) {
chi[i] = _chi(i);
}
return chi;
}
V<mint> multi_conv(int k, const V<int>& chi, const V<mint>& a, const V<mint>& b) {
int N = tens[k];
int S = 1;
while (S < 2 * N) S *= 2;
vector<vector<mint>> f(k, vector<mint>(S)), g(k, vector<mint>(S));
for (int i = 0; i < N; i++) {
f[chi[i] % k][i] = a[i];
}
for (int i = 0; i < N; i++) {
g[chi[i] % k][i] = b[i];
}
for (int j = 0; j < k; j++) {
butterfly(f[j]);
butterfly(g[j]);
}
vector<vector<mint>> fg(k, vector<mint>(S));
for (int l = 0; l < k; l++) {
for (int r = 0; r < k; r++) {
int lr = (l + r >= k) ? (l + r - k) : l + r;
for (int i = 0; i < S; i++) {
fg[lr][i] += f[l][i] * g[r][i];
}
}
}
for (int j = 0; j < k; j++) {
butterfly_inv(fg[j]);
}
V<mint> c(N);
const mint iS = mint(S).inv();
for (int i = 0; i < N; i++) {
c[i] = fg[chi[i] % k][i] * iS;
}
return c;
}
V<mint> pow_naive(int k, V<mint> a, ll m) {
int n = tens[k];
V<mint> res(n);
res[0] = 1;
auto chi = gen_chi(k);
while (m) {
if (m % 2) {
res = multi_conv(k, chi, res, a);
}
a = multi_conv(k, chi, a, a);
m /= 2;
}
return res;
}
V<mint> pow2(int k, V<mint> a, ll m) {
assert(a[0] == mint(1));
a[0] = 0;
auto chi = gen_chi(k);
int n = tens[k];
V<mint> b(n), c(n);
b[0] = 1;
mint choose = 1;
for (int h = 0; h <= k * 9; h++) {
if (h) choose = choose * (m - (h - 1)) / h;
// choose = C(m, h)
for (int i = 0; i < n; i++) {
c[i] += b[i] * choose;
}
b = multi_conv(k, chi, b, a);
}
for (auto x : b) assert(x == mint(0));
return c;
}
V<mint> pow(int k, V<mint> a, ll m) {
if (k == 0) {
return {a[0].pow(m)};
}
if (a[0] == 0) {
return pow_naive(k, a, min(64LL, m));
}
mint a0 = a[0];
mint ia0 = a0.inv();
for (auto& x: a) {
x *= ia0;
}
//a = pow_naive(k, a, m);
a = pow2(k, a, m);
mint a0m = a0.pow(m);
for (auto& x: a) {
x *= a0m;
}
return a;
}
int main() {
int n2, k, t;
ll m;
sc.read(n2, k, m, t);
int n = tens[k];
V<mint> a(n);
for (int i = 0; i < n2; i++) {
int x;
sc.read(x);
a[x] += 1;
}
for (int h = t; h < k; h++) {
for (int i = 0; i < n; i++) {
if (i / tens[h] % 10) continue;
V<mint> b(10);
for (int j = 0; j < 10; j++) {
b[j] = a[i + tens[h] * j];
}
b = fft10(b, g10);
for (int j = 0; j < 10; j++) {
a[i + tens[h] * j] = b[j];
}
}
}
for (int i = 0; i < tens[k - t]; i++) {
// convolute [TEN(t) * i .. TEN(t) * (i + 1)]
V<mint> c(a.begin() + tens[t] * i, a.begin() + tens[t] * (i + 1));
c = pow(t, c, m);
copy_n(c.begin(), tens[t], a.begin() + tens[t] * i);
}
for (int h = t; h < k; h++) {
for (int i = 0; i < n; i++) {
if (i / tens[h] % 10) continue;
V<mint> b(10);
for (int j = 0; j < 10; j++) {
b[j] = a[i + tens[h] * j];
}
b = fft10(b, ig10);
for (int j = 0; j < 10; j++) {
a[i + tens[h] * j] = b[j];
}
}
}
for (int i = 0; i < n; i++) {
a[i] /= mint(tens[k - t]);
pr.writeln(a[i].val());
}
return 0;
}