結果
| 問題 | No.1388 Less than K |
| ユーザー |
👑  PCTprobability
|
| 提出日時 | 2021-02-08 01:14:51 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 630 ms / 3,000 ms |
| コード長 | 32,840 bytes |
| コンパイル時間 | 3,909 ms |
| コンパイル使用メモリ | 252,712 KB |
| 実行使用メモリ | 25,068 KB |
| 最終ジャッジ日時 | 2023-09-18 03:21:32 |
| 合計ジャッジ時間 | 27,248 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / 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 | AC | 171 ms
23,024 KB |
| testcase_01 | AC | 170 ms
23,024 KB |
| testcase_02 | AC | 219 ms
23,232 KB |
| testcase_03 | AC | 171 ms
23,024 KB |
| testcase_04 | AC | 178 ms
23,036 KB |
| testcase_05 | AC | 189 ms
23,092 KB |
| testcase_06 | AC | 211 ms
23,152 KB |
| testcase_07 | AC | 220 ms
23,060 KB |
| testcase_08 | AC | 211 ms
23,028 KB |
| testcase_09 | AC | 180 ms
23,168 KB |
| testcase_10 | AC | 180 ms
23,032 KB |
| testcase_11 | AC | 177 ms
23,084 KB |
| testcase_12 | AC | 193 ms
23,088 KB |
| testcase_13 | AC | 196 ms
23,216 KB |
| testcase_14 | AC | 203 ms
23,040 KB |
| testcase_15 | AC | 212 ms
23,040 KB |
| testcase_16 | AC | 219 ms
23,044 KB |
| testcase_17 | AC | 220 ms
23,172 KB |
| testcase_18 | AC | 220 ms
23,032 KB |
| testcase_19 | AC | 219 ms
23,180 KB |
| testcase_20 | AC | 218 ms
23,372 KB |
| testcase_21 | AC | 176 ms
23,160 KB |
| testcase_22 | AC | 589 ms
24,740 KB |
| testcase_23 | AC | 182 ms
23,020 KB |
| testcase_24 | AC | 195 ms
23,268 KB |
| testcase_25 | AC | 204 ms
23,092 KB |
| testcase_26 | AC | 196 ms
23,172 KB |
| testcase_27 | AC | 191 ms
23,036 KB |
| testcase_28 | AC | 171 ms
23,152 KB |
| testcase_29 | AC | 171 ms
23,144 KB |
| testcase_30 | AC | 171 ms
23,152 KB |
| testcase_31 | AC | 171 ms
23,160 KB |
| testcase_32 | AC | 171 ms
23,208 KB |
| testcase_33 | AC | 610 ms
23,932 KB |
| testcase_34 | AC | 597 ms
25,068 KB |
| testcase_35 | AC | 596 ms
24,436 KB |
| testcase_36 | AC | 303 ms
23,436 KB |
| testcase_37 | AC | 621 ms
23,948 KB |
| testcase_38 | AC | 180 ms
23,164 KB |
| testcase_39 | AC | 176 ms
23,160 KB |
| testcase_40 | AC | 180 ms
23,076 KB |
| testcase_41 | AC | 186 ms
23,032 KB |
| testcase_42 | AC | 176 ms
23,028 KB |
| testcase_43 | AC | 223 ms
23,224 KB |
| testcase_44 | AC | 225 ms
23,092 KB |
| testcase_45 | AC | 224 ms
23,376 KB |
| testcase_46 | AC | 223 ms
23,268 KB |
| testcase_47 | AC | 223 ms
23,244 KB |
| testcase_48 | AC | 221 ms
23,320 KB |
| testcase_49 | AC | 224 ms
23,100 KB |
| testcase_50 | AC | 224 ms
23,172 KB |
| testcase_51 | AC | 223 ms
23,188 KB |
| testcase_52 | AC | 223 ms
23,228 KB |
| testcase_53 | AC | 185 ms
23,156 KB |
| testcase_54 | AC | 183 ms
23,032 KB |
| testcase_55 | AC | 174 ms
23,216 KB |
| testcase_56 | AC | 197 ms
23,212 KB |
| testcase_57 | AC | 221 ms
23,176 KB |
| testcase_58 | AC | 222 ms
23,168 KB |
| testcase_59 | AC | 221 ms
23,328 KB |
| testcase_60 | AC | 221 ms
23,108 KB |
| testcase_61 | AC | 316 ms
23,884 KB |
| testcase_62 | AC | 630 ms
24,876 KB |
| testcase_63 | AC | 175 ms
23,084 KB |
| testcase_64 | AC | 178 ms
23,160 KB |
| testcase_65 | AC | 181 ms
23,028 KB |
| testcase_66 | AC | 186 ms
23,092 KB |
| testcase_67 | AC | 188 ms
23,040 KB |
| testcase_68 | AC | 215 ms
23,180 KB |
| testcase_69 | AC | 222 ms
23,160 KB |
| testcase_70 | AC | 222 ms
23,096 KB |
| testcase_71 | AC | 222 ms
23,360 KB |
| testcase_72 | AC | 260 ms
23,612 KB |
| testcase_73 | AC | 311 ms
24,020 KB |
| testcase_74 | AC | 407 ms
24,748 KB |
| testcase_75 | AC | 603 ms
24,756 KB |
| testcase_76 | AC | 623 ms
24,824 KB |
ソースコード
#include <bits/stdc++.h>
using namespace std;
/*#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif*/
using ll = long long;
using ld = long double;
#define all(s) (s).begin(),(s).end()
#define vcin(n) for(ll i=0;i<ll(n.size());i++) cin>>n[i]
#define rep2(i, m, n) for (int i = (m); i < (n); ++i)
#define rep(i, n) rep2(i, 0, n)
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define se second
#define P pair<ll,ll>
const ll mod = 998244353;
//const ll mod = 1000000007;
const ll inf = 2000000000000000000ll;
static const long double pi = 3.141592653589793;
void YesNo(bool a){if(a){cout<<"Yes"<<endl;}else{cout<<"No"<<endl;}}
void YESNO(bool a){if(a){cout<<"YES"<<endl;}else{cout<<"NO"<<endl;}}
template<class T,class U> void chmax(T& t,const U& u){if(t<u) t=u;}
template<class T,class U> void chmin(T& t,const U& u){if(t>u) t=u;}
ll modPow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
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
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`
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);
} // namespace internal
} // namespace atcoder
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());
}
static_modint(bool 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());
}
dynamic_modint(bool 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, 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))];
}
}
}
} // 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) {
if (n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
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;
}
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
using namespace atcoder;
enum Mode {
FAST = 1,
NAIVE = -1,
};
template <class T, Mode mode = FAST>
struct FormalPowerSeries : std::vector<T> {
using std::vector<T>::vector;
using std::vector<T>::size;
using std::vector<T>::resize;
using F = FormalPowerSeries;
F &operator+=(F &g){
(*this).resize(max(int((*this).size()),int(g.size())));
for(int i=0;i<int(min((*this).size(),g.size()));i++){
(*this)[i]+=g[i];
}
return *this;
}
F &operator+=(const T &t){
assert(int((*this).size()));
(*this)[0]+=t;
return *this;
}
F &operator-=(const F &g) {
for(int i=0;i<int(min((*this).size(),g.size()));i++){
(*this)[i]-=g[i];
}
return *this;
}
F &operator-=(const T &t){
assert(int((*this).size()));
(*this)[0]-=t;
return *this;
}
F &operator*=(const T &g) {
for(int i=0;i<int((*this).size());i++){
(*this)[i]*=g;
}
return *this;
}
F &operator/=(const T &g) {
T div=g.inv();
for(int i=0;i<int((*this).size());i++){
(*this)[i]*=div;
}
return *this;
}
F &operator>>=(const int sz) const {
assert(sz >= 0);
int n = (*this).size();
(*this).erase((*this).begin(), (*this).begin() + std::min(sz, n));
(*this).resize(n);
return *this;
}
F &operator<<=(const int sz) const {
assert(sz >= 0);
int n = (*this).size();
(*this).insert((*this).begin(), (*this).begin() + sz, 0);
(*this).resize(n);
return *this;
}
F &operator=(const std::vector<T> &v) {
int n = (*this).size();
for(int i = 0; i < n; ++i) (*this)[i] = v[i];
return *this;
}
F operator-() const {
F ret = *this;
return ret * -1;
}
F &operator*=(F &g) {
if(mode==FAST) {
auto tmp=atcoder::convolution(*this,g);
(*this).resize(int(tmp.size()));
for(int i=0;i<int(tmp.size());++i){
(*this)[i]=tmp[i];
}
return *this;
}
else{
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 inv(int deg = 400010) const {
int n = (*this).size();
assert(mode == FAST and n and (*this)[0] != 0);
if(deg == -1) deg = n;
assert(deg > 0);
F res{(*this)[0].inv()};
while(int(res.size()) < deg) {
int m = res.size();
F f((*this).begin(), (*this).begin() + std::min(n, m * 2)), r(res);
f.resize(m * 2), atcoder::internal::butterfly(f);
r.resize(m * 2), atcoder::internal::butterfly(r);
for(int i = 0; i < m * 2; ++i) f[i] *= r[i];
atcoder::internal::butterfly_inv(f);
f.erase(f.begin(), f.begin() + m);
f.resize(m * 2), atcoder::internal::butterfly(f);
for(int i = 0; i < m * 2; ++i) f[i] *= r[i];
atcoder::internal::butterfly_inv(f);
T iz = T(m * 2).inv();
iz *= -iz;
for(int i = 0; i < m; ++i) f[i] *= iz;
res.insert(res.end(), f.begin(), f.begin() + m);
}
res.resize(deg);
return res;
}
F &operator/=(const F &g) {
if(mode == FAST){
int n = (*this).size();
(*this).resize(400010);
g.inv();
(*this) = atcoder::convolution(*this,g);
return *this;
}
else{
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;
}
}
F &operator%=(const F &g) { return *this-=*this/g*g; }
F operator*(const T &g) const { return F(*this)*=g;}
F operator-(const T &g) const { return F(*this)-=g;}
F operator*(F &g) { return F(*this)*=g;}
F operator-(const F &g) const { return F(*this)-=g;}
F operator+(F &g) { return F(*this)+=g;}
F operator/(const F &g) const { return F(*this)/=g;}
F operator%(const F &g) const { return F(*this)%=g;}
F operator<<(const int d) const { return F(*this)<<=d;}
F operator>>(const int d) const { return F(*this)>>=d;}
T eval(const T &t) const {
int n = (*this).size();
T res = 0, tmp = 1;
for(int i = 0; i < n; ++i){
res += (*this)[i] * tmp, tmp *= t;
}
return res;
}
F &diff_inplace() {
int n = (*this).size();
for(int i = 1; i < n; ++i) (*this)[i - 1] = (*this)[i] * i;
(*this)[n - 1] = 0;
return *this;
}
F diff() const { F(*this).diff_inplace();}
F &integral_inplace() {
int n = (*this).size(), mod = T::mod();
std::vector<T> inv(n);
{
inv[1] = 1;
for(int i = 2; i < n; ++i)
inv[i] = T(mod) - inv[mod % i] * (mod / i);
}
for(int i = n - 2; i >= 0; --i) (*this)[i + 1] = (*this)[i] * inv[i + 1];
(*this)[0] = 0;
return *this;
}
F integral() const { return F(*this).integral_inplace(); }
F &log_inplace() {
int n = (*this).size();
assert(n and (*this)[0] == 1);
F f_inv = (*this).inv();
(*this).diff_inplace();
(*this) *= f_inv;
(*this).integral_inplace();
return *this;
}
F log() const { return F(*this).log_inplace(); }
F &deriv_inplace() {
int n = (*this).size();
assert(n);
for(int i = 2; i < n; ++i) (*this)[i] *= i;
(*this).erase((*this).begin());
(*this).push_back(0);
return *this;
}
F deriv() const { return F(*this).deriv_inplace(); }
F &exp_inplace() {
int n = (*this).size();
assert(n and (*this)[0] == 0);
F g{1};
(*this)[0] = 1;
F h_drv((*this).deriv());
for(int m = 1; m < n; m *= 2) {
F f((*this).begin(), (*this).begin() + m);
f.resize(2 * m), atcoder::internal::butterfly(f);
auto mult_f = [&](F &p) {
p.resize(2 * m);
atcoder::internal::butterfly(p);
for(int i = 0; i < 2 * m; ++i) p[i] *= f[i];
atcoder::internal::butterfly_inv(p);
p /= 2 * m;
};
if(m > 1) {
F g_(g);
g_.resize(2 * m), atcoder::internal::butterfly(g_);
for(int i = 0; i < 2 * m; ++i) g_[i] *= g_[i] * f[i];
atcoder::internal::butterfly_inv(g_);
T iz = T(-2 * m).inv();
g_ *= iz;
g.insert(g.end(), g_.begin() + m / 2, g_.begin() + m);
}
F t((*this).begin(), (*this).begin() + m);
t.deriv_inplace();
{
F r{h_drv.begin(), h_drv.begin() + m - 1};
mult_f(r);
for(int i = 0; i < m; ++i) t[i] -= r[i] + r[m + i];
}
t.insert(t.begin(), t.back());
t.pop_back();
t *= g;
F v((*this).begin() + m, (*this).begin() + std::min(n, 2 * m));
v.resize(m);
t.insert(t.begin(), m - 1, 0);
t.push_back(0);
t.integral_inplace();
for(int i = 0; i < m; ++i) v[i] -= t[m + i];
mult_f(v);
for(int i = 0; i < std::min(n - m, m); ++i)
(*this)[m + i] = v[i];
}
return *this;
}
F exp() const { return F(*this).exp_inplace(); }
F &pow_inplace(long long k) {
int n = (*this).size(), l = 0;
assert(k >= 0);
if(!k){
for(int i = 0; i < n; ++i) (*this)[i] = !i;
return *this;
}
while(l < n and (*this)[l] == 0) ++l;
if(l > (n - 1) / k or l == n) return *this = F(n);
T c = (*this)[l];
(*this).erase((*this).begin(), (*this).begin() + l);
(*this) /= c;
(*this).log_inplace();
(*this).resize(n - l * k);
(*this) *= k;
(*this).exp_inplace();
(*this) *= c.pow(k);
(*this).insert((*this).begin(), l * k, 0);
return *this;
}
F pow(const long long k) const { return F(*this).pow_inplace(); }
};
using fps = FormalPowerSeries<atcoder::modint998244353, FAST>;
vector<vector<fps>> multi(vector<vector<fps>> &a,vector<vector<fps>> &b){
fps f={0};
vector<vector<fps>> c(a.size(),vector<fps>(b[0].size(),f));
for(int i=0;i<int(a.size());i++){
for(int k=0;k<int(b.size());k++){
for(int j=0;j<int(b[0].size());j++){
auto r=a[i][k]*b[k][j];
c[i][j]+=r;
// c[i][j]+=(a[i][k] * b[k][j]));
}
}
}
return c;
}
vector<vector<fps>> mul_exp(vector<vector<fps>> adj, ll k){
if (k == 1) return adj;
vector<vector<fps>> res(int(adj.size()),vector<fps>(int(adj[0].size())));
fps f={1};
for(int i=0;i<int(adj.size());i++){
res[i][i]=f;
}
while(k>0){
if(k&1) res=multi(adj,res);
adj=multi(adj,adj);
k/=2;
}
return res;
}
constexpr ll MAX = 500000;
ll fac[MAX],finv[MAX],inv[MAX];
void COMinit(){
fac[0]=fac[1]=1;
finv[0]=finv[1]=1;
inv[1]=1;
for(int i=2;i<MAX;i++){
fac[i]=fac[i-1]*i%mod;
inv[i]=mod-inv[mod%i]*(mod/i)%mod;
finv[i]=finv[i-1]*inv[i]%mod;
}
}
ll COM(int n,int k){
if(n<k) return 0;
if(n<0||k<0) return 0;
return fac[n]*(finv[k]*finv[n-k]%mod)%mod;
}
ll HOM(ll n,ll k){
if(n+k-1>=n-1&&n-1>=0){
return COM(n+k-1,n-1);
}
else{
return 0;
}
}
fps bunsi(ll a){
fps f1={1};
fps f2={0,1};
fps f3={0};
vector<vector<fps>> f={{f1,f2},{f1,f3}};
auto p=mul_exp(f,a-1);
for(int i=0;i<int(p[0][0].size());i++){
if(i%2==1){
p[0][0][i]*=-1;
}
}
return p[0][0];
}
ll q(ll a,ll b){
return (a*fac[a-b-1]%mod)*modPow(fac[b]*fac[a-2*b]%mod,mod-2,mod)%mod;
}
fps bunbo(ll a){
fps f(a/2+1);
for(int i=0;i<=a/2;i++){
f[i]=q(a,i);
if(i%2==1){
f[i]*=-1;
}
}
return f;
}
fps query(ll a){
a++;
auto p=bunbo(a);
auto q=bunsi(a);
// p/=q;
// p=p.inv();
p=p.inv();
q*=p;
return q;
}
using mint = atcoder::modint998244353;
int main() {
/* mod は 1e9+7 */
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
cout<< fixed << setprecision(10);
COMinit();
ll h,w,k;
cin>>h>>w>>k;
h--;
w--;
mint ans=0;
fps z=query(k/2);
for(int i=0;i<=(h+w)/2;i++){
ll p=i*2;
ll a=h-i;
ll b=w-i;
ll tmp=COM(a+b+p,p)*COM(a+b,a)%mod;
mint ai=z[i]*tmp;
ans+=ai;
// cout<<z[i].val()<<endl;
}
cout<<ans.val()<<endl;
}