結果
| 問題 | No.2527 H and W |
| ユーザー |
 Gandalfr
|
| 提出日時 | 2023-11-03 22:05:21 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 616 ms / 2,000 ms |
| コード長 | 41,877 bytes |
| コンパイル時間 | 4,455 ms |
| コンパイル使用メモリ | 261,392 KB |
| 実行使用メモリ | 78,300 KB |
| 最終ジャッジ日時 | 2024-09-25 20:27:59 |
| 合計ジャッジ時間 | 20,990 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（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 | 596 ms
74,080 KB |
| testcase_01 | AC | 570 ms
74,196 KB |
| testcase_02 | AC | 600 ms
78,168 KB |
| testcase_03 | AC | 583 ms
74,204 KB |
| testcase_04 | AC | 591 ms
78,168 KB |
| testcase_05 | AC | 583 ms
74,200 KB |
| testcase_06 | AC | 592 ms
78,296 KB |
| testcase_07 | AC | 586 ms
74,072 KB |
| testcase_08 | AC | 616 ms
78,296 KB |
| testcase_09 | AC | 610 ms
78,168 KB |
| testcase_10 | AC | 596 ms
78,168 KB |
| testcase_11 | AC | 589 ms
74,072 KB |
| testcase_12 | AC | 586 ms
78,300 KB |
| testcase_13 | AC | 592 ms
78,168 KB |
| testcase_14 | AC | 596 ms
78,168 KB |
| testcase_15 | AC | 588 ms
74,072 KB |
| testcase_16 | AC | 606 ms
78,168 KB |
| testcase_17 | AC | 593 ms
78,168 KB |
| testcase_18 | AC | 600 ms
78,164 KB |
| testcase_19 | AC | 596 ms
78,164 KB |
| testcase_20 | AC | 601 ms
78,296 KB |
| testcase_21 | AC | 587 ms
78,168 KB |
| testcase_22 | AC | 585 ms
78,300 KB |
| testcase_23 | AC | 587 ms
78,164 KB |
| testcase_24 | AC | 590 ms
78,296 KB |
| testcase_25 | AC | 588 ms
78,168 KB |
ソースコード
#line 1 "playspace/main.cpp"
#include <bits/stdc++.h>
#line 4 "library/gandalfr/math/Eratosthenes.hpp"
#line 6 "library/gandalfr/math/Eratosthenes.hpp"
#line 6 "library/gandalfr/math/enumeration_utility.hpp"
#line 1 "library/atcoder/modint.hpp"
#line 6 "library/atcoder/modint.hpp"
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#line 1 "library/atcoder/internal_math.hpp"
#line 5 "library/atcoder/internal_math.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
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;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
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;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
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);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
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};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
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
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
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);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
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;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#line 1 "library/atcoder/internal_type_traits.hpp"
#line 7 "library/atcoder/internal_type_traits.hpp"
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
#line 14 "library/atcoder/modint.hpp"
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
#line 4 "library/gandalfr/math/formal_power_series.hpp"
#line 1 "library/atcoder/convolution.hpp"
#line 9 "library/atcoder/convolution.hpp"
#line 1 "library/atcoder/internal_bit.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
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
#line 12 "library/atcoder/convolution.hpp"
namespace atcoder {
namespace internal {
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for (int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for (int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 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()) *
inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
}
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;
// B = 2^63, -B <= x, r(real value) < B
// (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
// r = c1[i] (mod MOD1)
// focus on MOD1
// r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
// r = x,
// x - M' + (0 or 2B),
// x - 2M' + (0, 2B or 4B),
// x - 3M' + (0, 2B, 4B or 6B) (without mod!)
// (r - x) = 0, (0)
// - M' + (0 or 2B), (1)
// -2M' + (0 or 2B or 4B), (2)
// -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
// we checked that
// ((1) mod MOD1) mod 5 = 2
// ((2) mod MOD1) mod 5 = 3
// ((3) mod MOD1) mod 5 = 4
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
#line 7 "library/gandalfr/math/formal_power_series.hpp"
// https://web.archive.org/web/20220813112322/https://opt-cp.com/fps-implementation/#toc2
template<class T> struct FormalPowerSeries : public std::vector<T> {
using std::vector<T>::vector;
using std::vector<T>::operator=;
using F = FormalPowerSeries;
F operator-() const {
F res(*this);
for (auto &e : res) e = -e;
return res;
}
F &operator*=(const T &g) {
for (auto &e : *this) e *= g;
return *this;
}
F &operator/=(const T &g) {
assert(g != T(0));
*this *= g.inv();
return *this;
}
F &operator+=(const F &g) {
int n = (*this).size(), m = g.size();
for(int i = 0; i < std::min(n, m); ++i) (*this)[i] += g[i];
return *this;
}
F &operator-=(const F &g) {
int n = (*this).size(), m = g.size();
for(int i = 0; i < std::min(n, m); ++i) (*this)[i] -= g[i];
return *this;
}
F &operator<<=(const int d) {
int n = (*this).size();
(*this).insert((*this).begin(), d, 0);
(*this).resize(n);
return *this;
}
F &operator>>=(const int d) {
int n = (*this).size();
(*this).erase((*this).begin(), (*this).begin() + std::min(n, d));
(*this).resize(n);
return *this;
}
F inv(int d = -1) const {
int n = (*this).size();
assert(n != 0 && (*this)[0] != 0);
if (d == -1) d = n;
assert(d > 0);
F res{(*this)[0].inv()};
while ((int)res.size() < d) {
int m = size(res);
F f(begin(*this), begin(*this) + std::min(n, 2*m));
F r(res);
f.resize(2*m), atcoder::internal::butterfly(f);
r.resize(2*m), atcoder::internal::butterfly(r);
for(int i = 0; i < 2 * m; ++i) f[i] *= r[i];
atcoder::internal::butterfly_inv(f);
f.erase(f.begin(), f.begin() + m);
f.resize(2*m), atcoder::internal::butterfly(f);
for(int i = 0; i < 2 * m; ++i) f[i] *= r[i];
atcoder::internal::butterfly_inv(f);
T iz = T(2*m).inv(); iz *= -iz;
for(int i = 0; i < m; ++i) f[i] *= iz;
res.insert(res.end(), f.begin(), f.begin() + m);
}
return {res.begin(), res.begin() + d};
}
// fast: FMT-friendly modulus only
F &operator*=(const F &g) {
int n = (*this).size();
*this = convolution(*this, g);
(*this).resize(n);
return *this;
}
F &operator/=(const F &g) {
int n = (*this).size();
*this = convolution(*this, g.inv(n));
(*this).resize(n);
return *this;
}
// naive
F &naive_mult(const F &g) {
int n = (*this).size(), m = g.size();
for(int i = n - 1; i >= 0; --i) {
(*this)[i] *= g[0];
for(int j = 1; j < std::min(i+1, m); ++j) (*this)[i] += (*this)[i-j] * g[j];
}
return *this;
}
F &naive_div(const F &g) {
assert(g[0] != T(0));
T ig0 = g[0].inv();
int n = (*this).size(), m = g.size();
for(int i = 0; i < n; ++i) {
for(int j = 1; j < std::min(i+1, m); ++j) (*this)[i] -= (*this)[i-j] * g[j];
(*this)[i] *= ig0;
}
return *this;
}
// sparse
F &sparse_mult(const std::vector<std::pair<int, T>> &g) {
int n = (*this).size();
auto [d, c] = g.front();
if (d == 0) g.erase(g.begin());
else c = 0;
for(int i = n - 1; i >= 0; --i) {
(*this)[i] *= c;
for (auto &[j, b] : g) {
if (j > i) break;
(*this)[i] += (*this)[i-j] * b;
}
}
return *this;
}
F &sparse_div(const std::vector<std::pair<int, T>> &g) {
int n = (*this).size();
auto [d, c] = g.front();
assert(d == 0 && c != T(0));
T ic = c.inv();
g.erase(g.begin());
for(int i = 0; i < n; ++i) {
for (auto &[j, b] : g) {
if (j > i) break;
(*this)[i] -= (*this)[i-j] * b;
}
(*this)[i] *= ic;
}
return *this;
}
F &operator^=(long long n) {
if (n == 0) {
std::fill(this->begin(), this->end(), T(0));
(*this)[0] = 1;
return *this;
}
F f(*this);
--n;
while (n > 0) {
if (n & 1)
*this *= f;
f = f * f;
n >>= 1;
}
return *this;
}
// multiply and divide (1 + cz^d)
void multiply(const int d, const T c) {
int n = (*this).size();
if (c == T(1)) for(int i = n - d - 1; i >= 0; --i) (*this)[i+d] += (*this)[i];
else if (c == T(-1)) for(int i = n - d - 1; i >= 0; --i) (*this)[i+d] -= (*this)[i];
else for(int i = n - d - 1; i >= 0; --i) (*this)[i+d] += (*this)[i] * c;
}
void divide(const int d, const T c) {
int n = (*this).size();
if (c == T(1)) for(int i = 0; i < n - d; ++i) (*this)[i+d] -= (*this)[i];
else if (c == T(-1)) for(int i = 0; i < n - d; ++i) (*this)[i+d] += (*this)[i];
else for(int i = 0; i < n - d; ++i) (*this)[i+d] -= (*this)[i] * c;
}
T eval(const T &a) const {
T x(1), res(0);
for (auto e : *this) res += e * x, x *= a;
return res;
}
friend F operator*(const T &g, const F &f) { return F(f) *= g; }
friend F operator/(const T &g, const F &f) { return F(f) /= g; }
friend F operator+(const F &f1, const F &f2) { return F(f1) += f2; }
friend F operator-(const F &f1, const F &f2) { return F(f1) -= f2; }
friend F operator<<(const F &f, const int d) { return F(f) <<= d; }
friend F operator>>(const F &f, const int d) { return F(f) >>= d; }
friend F operator*(const F &f1, const F &f2) { return F(f1) *= f2; }
friend F operator/(const F &f1, const F &f2) { return F(f1) /= f2; }
friend F operator*(const F &f, const std::vector<std::pair<int, T>> &g) { return F(f) *= g; }
friend F operator/(const F &f, const std::vector<std::pair<int, T>> &g) { return F(f) /= g; }
friend F operator^(const F &f, long long g) { return F(f) ^= g; }
};
#line 9 "library/gandalfr/math/enumeration_utility.hpp"
template <class T> T power(T x, long long n) {
T ret = static_cast<T>(1);
while (n > 0) {
if (n & 1)
ret = ret * x;
x = x * x;
n >>= 1;
}
return ret;
}
long long power(long long x, long long n) {
long long ret = 1;
while (n > 0) {
if (n & 1)
ret = ret * x;
x = x * x;
n >>= 1;
}
return ret;
}
long long power(long long x, long long n, int MOD) {
long long ret = 1;
x %= MOD;
while (n > 0) {
if (n & 1)
ret = ret * x % MOD;
x = x * x % MOD;
n >>= 1;
}
return ret;
}
long long power(long long x, long long n, long long MOD) {
long long ret = 1;
x %= MOD;
while (n > 0) {
if (n & 1)
ret = (__int128_t)ret * x % MOD;
x = (__int128_t)x * x % MOD;
n >>= 1;
}
return ret;
}
template <int m> class factorial {
private:
static inline std::vector<atcoder::static_modint<m>> fact{1};
public:
factorial() = delete;
~factorial() = delete;
static atcoder::static_modint<m> get(int n) {
while (n >= (int)fact.size())
fact.push_back(fact.back() * fact.size());
return fact[n];
}
};
atcoder::modint1000000007 (*fact1000000007)(int) = factorial<1000000007>::get;
atcoder::modint998244353 (*fact998244353)(int) = factorial<998244353>::get;
template <int m> static atcoder::static_modint<m> permutation(int n, int k) {
assert(0 <= k && k <= n);
return factorial<m>::get(n) / factorial<m>::get(n - k);
}
atcoder::modint1000000007 (*perm1000000007)(int, int) = permutation<1000000007>;
atcoder::modint998244353 (*perm998244353)(int, int) = permutation<998244353>;
template <int m> static atcoder::static_modint<m> combnation(int n, int k) {
assert(0 <= k && k <= n);
return factorial<m>::get(n) /
(factorial<m>::get(k) * factorial<m>::get(n - k));
}
atcoder::modint1000000007 (*comb1000000007)(int, int) = combnation<1000000007>;
atcoder::modint998244353 (*comb998244353)(int, int) = combnation<998244353>;
template <int m> static FormalPowerSeries<atcoder::static_modint<m>> Bernoulli_number(int n) {
assert(0 <= n);
FormalPowerSeries<atcoder::static_modint<m>> F(n, 0);
F[0] = 1;
for (int i = 1; i < n; ++i) {
F[i] = F[i - 1] / (i + 1);
}
F = F.inv();
for (int i = 0; i < n; ++i) {
F[i] *= factorial<m>::get(i);
}
return F;
}
FormalPowerSeries<atcoder::modint998244353> (*Bernoulli998244353)(int) = Bernoulli_number<998244353>;
#line 8 "library/gandalfr/math/Eratosthenes.hpp"
/**
* @see https://drken1215.hatenablog.com/entry/2023/05/23/233000
*/
bool MillerRabin(long long N, const std::vector<long long> &A) {
long long s = 0, d = N - 1;
while (d % 2 == 0) {
++s;
d >>= 1;
}
for (auto a : A) {
if (N <= a)
return true;
long long t, x = power(a, d, N);
if (x != 1) {
for (t = 0; t < s; ++t) {
if (x == N - 1)
break;
x = (__int128_t)x * x % N;
}
if (t == s)
return false;
}
}
return true;
}
/**
* @brief 素数判定や列挙をサポートするクラス
* @brief 素数篩を固定サイズで構築、それをもとに素数列挙などを行う
* @attention 構築サイズが (2^23) でおよそ 0.5s
*/
class Eratosthenes {
protected:
static inline int seive_size = (1 << 23);
static inline std::vector<bool> sieve;
static inline std::vector<int> primes{2, 3}, movius, min_factor;
static void make_table() {
sieve.assign(seive_size, true);
sieve[0] = sieve[1] = false;
movius.assign(seive_size, 1);
min_factor.assign(seive_size, 1);
for (int i = 2; i <= seive_size; ++i) {
if (!sieve[i])
continue;
movius[i] = -1;
min_factor[i] = i;
primes.push_back(i);
for (int j = i * 2; j < seive_size; j += i) {
sieve[j] = false;
movius[j] = ((j / i) % i == 0 ? 0 : -movius[j]);
if (min_factor[j] == 1)
min_factor[j] = i;
}
}
}
static std::vector<std::pair<long long, int>> fast_factorize(long long n) {
std::vector<std::pair<long long, int>> ret;
while (n > 1) {
if (ret.empty() || ret.back().first != min_factor[n]) {
ret.push_back({min_factor[n], 1});
} else {
ret.back().second++;
}
n /= min_factor[n];
}
return ret;
}
static std::vector<std::pair<long long, int>> naive_factorize(long long n) {
std::vector<std::pair<long long, int>> ret;
for (long long p : primes) {
if (n == 1 || p * p > n)
break;
while (n % p == 0) {
if (ret.empty() || ret.back().first != p)
ret.push_back({p, 1});
else
ret.back().second++;
n /= p;
}
}
if (n != 1)
ret.push_back({n, 1});
return ret;
}
public:
Eratosthenes() = delete;
~Eratosthenes() = delete;
static void set_sieve_size(int size) {
assert(sieve.empty());
seive_size = size;
}
/**
* @brief n が素数かを判定
*/
static bool is_prime(long long n) {
if (sieve.empty())
make_table();
assert(1 <= n);
if (n > 2 && (n & 1LL) == 0) {
return false;
} else if (n < seive_size) {
return sieve[n];
} else if (n < 4759123141LL) {
return MillerRabin(n, {2, 7, 61});
} else {
return MillerRabin(
n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}
}
/**
* @brief 素因数分解する
* @return factorize(p1^e1 * p2^e2 * ...) => {{p1, e1}, {p2, e2], ...},
* @return factorize(1) => {}
*/
static std::vector<std::pair<long long, int>> factorize(long long n) {
if (sieve.empty())
make_table();
assert(1 <= n);
if (n < seive_size) {
return fast_factorize(n);
} else {
return naive_factorize(n);
}
}
static int Movius(int n) {
if (movius.empty())
make_table();
assert(1 <= n);
return movius.at(n);
}
/**
* @brief 約数列挙
* @attention if n < sieve_size : O(N^(1/loglogN))
*/
template <bool sort = true>
static std::vector<long long> divisors(long long n) {
std::vector<long long> ds;
auto facs(factorize(n));
auto rec = [&](auto self, long long d, int cu) -> void {
if (cu == (int)facs.size()) {
ds.push_back(d);
return;
}
for (int e = 0; e <= facs[cu].second; ++e) {
self(self, d, cu + 1);
d *= facs[cu].first;
}
};
rec(rec, 1LL, 0);
if constexpr (sort)
std::sort(ds.begin(), ds.end());
return ds;
;
}
/**
* @brief オイラーのトーシェント関数
*/
static long long totient(long long n) {
long long ret = 1;
for (auto [b, e] : factorize(n))
ret *= power(b, e - 1) * (b - 1);
return ret;
}
static int kth_prime(int k) { return primes.at(k); }
};
#line 8 "library/gandalfr/other/io_supporter.hpp"
#line 10 "library/gandalfr/other/io_supporter.hpp"
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
for (int i = 0; i < (int)v.size(); i++)
os << v[i] << (i + 1 != (int)v.size() ? " " : "");
return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::set<T> &st) {
for (const T &x : st) {
std::cout << x << " ";
}
return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::multiset<T> &st) {
for (const T &x : st) {
std::cout << x << " ";
}
return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::deque<T> &dq) {
for (const T &x : dq) {
std::cout << x << " ";
}
return os;
}
template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &p) {
os << p.first << ' ' << p.second;
return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, std::queue<T> &q) {
int sz = q.size();
while (--sz) {
os << q.front() << ' ';
q.push(q.front());
q.pop();
}
os << q.front();
q.push(q.front());
q.pop();
return os;
}
namespace atcoder {
template <int m>
std::ostream &operator<<(std::ostream &os, const static_modint<m> &mi) {
os << mi.val();
return os;
}
template <int m>
std::ostream &operator<<(std::ostream &os, const dynamic_modint<m> &mi) {
os << mi.val();
return os;
}
}
template <typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
for (T &in : v)
is >> in;
return is;
}
template <typename T1, typename T2>
std::istream &operator>>(std::istream &is, std::pair<T1, T2> &p) {
is >> p.first >> p.second;
return is;
}
namespace atcoder {
template <int m>
std::istream &operator>>(std::istream &is, static_modint<m> &mi) {
long long n;
is >> n;
mi = n;
return is;
}
template <int m>
std::istream &operator>>(std::istream &is, dynamic_modint<m> &mi) {
long long n;
is >> n;
mi = n;
return is;
}
}
#line 5 "playspace/main.cpp"
using namespace std;
using ll = long long;
const int INF = 1001001001;
const ll INFLL = 1001001001001001001;
const ll MOD = 1000000007;
const ll _MOD = 998244353;
#define rep(i, j, n) for(ll i = (ll)(j); i < (ll)(n); i++)
#define rrep(i, j, n) for(ll i = (ll)(n-1); i >= (ll)(j); i--)
#define all(a) (a).begin(),(a).end()
#define debug(a) std::cerr << #a << ": " << a << std::endl
#define LF cout << endl
template<typename T1, typename T2> inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template<typename T1, typename T2> inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }
void Yes(bool ok){ std::cout << (ok ? "Yes" : "No") << std::endl; }
int main(void){
ll H, W, K;
cin >> H >> W >> K;
atcoder::modint998244353 ans = 0;
for (auto h: Eratosthenes::divisors(K)) {
auto w = K / h;
if (h <= H && w <= W) {
ans += comb998244353(H, h) * comb998244353(W, w);
}
}
cout << ans << endl;
}