結果
問題 | No.2527 H and W |
ユーザー |
👑 |
提出日時 | 2023-02-28 21:37:28 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 107 ms / 2,000 ms |
コード長 | 29,330 bytes |
コンパイル時間 | 3,319 ms |
コンパイル使用メモリ | 261,740 KB |
実行使用メモリ | 26,772 KB |
最終ジャッジ日時 | 2024-09-23 07:24:15 |
合計ジャッジ時間 | 6,898 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 23 |
ソースコード
#line 2 "/home/seekworser/.cpp_lib/competitive_library/competitive/std/std.hpp"#include <bits/stdc++.h>#ifndef LOCAL_TEST#pragma GCC target ("avx")#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")#endif // LOCAL_TESTusing namespace std;// 型名の短縮using ll = long long;using pii = pair<int, int>; using pll = pair<ll, ll>;using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>;using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>;using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;using vs = vector<string>; using vvs = vector<vector<string>>; using vvvs = vector<vector<vector<string>>>;template <class T> using priority_queue_min = priority_queue<T, vector<T>, greater<T>>;// 定数の定義constexpr double PI = 3.14159265358979323;constexpr int INF = 100100111; constexpr ll INFL = 3300300300300300491LL;float EPS = 1e-8; double EPSL = 1e-16;bool eq(const double x, const double y) { return abs(x - y) < EPSL; }bool eq(const float x, const float y) { return abs(x - y) < EPS; }template<typename T> bool eq(const T x, const T y) { return x == y; }template<typename T> bool neq(const T x, const T y) { return !(eq(x, y)); }template<typename T> bool ge(const T x, const T y) { return eq(x, y) || (x > y); }template<typename T> bool le(const T x, const T y) { return eq(x, y) || (x < y); }template<typename T> bool gt(const T x, const T y) { return !(le(x, y)); }template<typename T> bool lt(const T x, const T y) { return !(ge(x, y)); }constexpr int MODINT998244353 = 998244353;constexpr int MODINT1000000007 = 1000000007;// 入出力高速化struct Nyan { Nyan() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } nyan;// 汎用マクロの定義#define all(a) (a).begin(), (a).end()#define sz(x) ((int)(x).size())#define rep(i, n) for(ll i = 0, i##_len = ll(n); i < i##_len; ++i) // 0 から n-1 まで昇順#define repi(i, s, t) for(ll i = ll(s), i##_end = ll(t); i < i##_end; ++i) // s から t まで昇順#define repis(i, s, t, step) for(ll i = ll(s), i##_end = ll(t); i < i##_end; i+=step) // s から t まで stepずつ#define repir(i, s, t, step) for(ll i = ll(s), i##_end = ll(t); i > i##_end; i+=step) // s から t まで stepずつ#define repe(a, v) for(auto& a : (v)) // v の全要素(変更可能)#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod#define sdiv(n, m) (((n) - smod(n, m)) / (m)) // 非負div#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去void Yes(bool b) { cout << (b ? "Yes\n" : "No\n"); return; };void YES(bool b) { cout << (b ? "YES\n" : "NO\n"); return; };template<typename T, size_t N> T max(array<T, N>& a) { return *max_element(all(a)); };template<typename T, size_t N> T min(array<T, N>& a) { return *min_element(all(a)); };template<typename T> T max(vector<T>& a) { return *max_element(all(a)); };template<typename T> T min(vector<T>& a) { return *min_element(all(a)); };template<typename T> T sum(vector<T>& a, T zero = T(0)) { T rev = zero; rep(i, sz(a)) rev += a[i]; return rev; };// modでのpowll powm(ll a, ll n, ll mod=INFL) {ll res = 1;while (n > 0) {if (n & 1) res = (res * a) % mod;if (n > 1) a = (a * a) % mod;n >>= 1;}return res;}// 整数Sqrtll sqrtll(ll x) {assert(x >= 0);ll hi(x), lo(0);while (hi != lo) {ll y = (hi + lo + 1) / 2;if (y <= x/y) lo = y;else hi = y - 1;}return lo;}template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら trueを返す)template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら trueを返す)int digit(ll x, int d=10) { int rev=0; while (x > 0) { rev++; x /= d;}; return rev; } // xのd進数桁数/*** @brief std.hpp* @docs docs/std/std.md*/#line 3 "/home/seekworser/.cpp_lib/competitive_library/competitive/math/prime.hpp"template <class T> bool is_prime(T n) {if (n == 1) return false;for (T i=2; i <= (T)std::sqrt(n); i++) {if (n % i == 0) return false;}return true;};//return all devisortemplate <class T> vector<T> divisor(T n, bool sorted=true) {vector<T> ans(0);for (T i = 1; i <= (T)std::sqrt(n); i++) {if (n % i == 0) {ans.push_back(i);if (i * i != n) ans.push_back(n / i);}}if (sorted) sort(ans.begin(), ans.end());return ans;};template <class T> vector<T> prime_factor(T n) {vector<T> ans(0);for (T i = 2; i <= (T)std::sqrt(n); i++) {while (n % i == 0) {ans.push_back(i);n /= i;}}if (n != 1) ans.push_back(n);return ans;};template <class T> map<T, T> prime_factor_c(T n) {map<T, T> ans;for (T i = 2; i <= (T)std::sqrt(n); i++) {while (n % i == 0) {ans[i] += 1;n /= i;}}if (n != 1) ans[n] += 1;return ans;};template <class T> vector<T> primes(T n) {vector<T> ans(0);if (n < 2) return ans;vector<bool> is_primev(n+1, true);is_primev.at(0) = is_primev.at(1) = false;for (T i = 2; i <= (T)std::sqrt(n); i++) {if (!is_primev.at(i)) continue;for (T j = i*2; j <= n; j+=i) is_primev.at(j) = false;}for (T i = 2; i <= n; i++) {if (is_primev.at(i)) ans.push_back(i);}return ans;};template <class T> vector<T> segment_seive(T s, T t) {vector<T> ans(0);if (t < 2 || s < 0 || s >= t) return ans;vector<bool> is_prime_small((T)std::sqrt(t)+1, true);vector<bool> is_prime_large(t-s, true);for (T i = 2; i <= (T)std::sqrt(t); i++) {if (!is_prime_small.at(i)) continue;for (T j = i*2; j*j < t; j+=i) is_prime_small.at(j) = false;for (T j = max(2*i, ((s+i-1)/i)*i); j < t; j+=i) is_prime_large.at(j-s) = false;}for (T i=0; i < t-s; i++) {if (is_prime_large.at(i) && s+i != 1) ans.push_back(s+i);}return ans;};/*** @brief prime.hpp* @docs docs/math/prime.md*/#line 3 "/home/seekworser/.cpp_lib/competitive_library/competitive/math/combination.hpp"struct Combination {ll pm;vl fact, fact_inv;Combination(int n = 1000003, ll p = 998244353) : fact(n), fact_inv(n){vl inv(n);pm = p;fact[0] = fact[1] = 1;fact_inv[0] = fact_inv[1] = 1;inv[0] = 0;inv[1] = 1;for (int i = 2; i < n; i++) {fact[i] = fact[i - 1] * i % p;inv[i] = p - inv[p % i] * (p / i) % p;fact_inv[i] = fact_inv[i - 1] * inv[i] % p;}}ll operator()(int n, int r) {if (r < 0 || n < r) return 0;return fact[n] * (fact_inv[r] * fact_inv[n - r] % pm) % pm;}};/*** @brief combination.hpp* @docs docs/math/combination.md*/#line 4 "/home/seekworser/.cpp_lib/competitive_library/atcoder/modint.hpp"#include <type_traits>#ifdef _MSC_VER#include <intrin.h>#endif#line 3 "/home/seekworser/.cpp_lib/competitive_library/atcoder/internal_math.hpp"#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {// @param m `1 <= m`// @return x mod mconstexpr 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 Lakestruct 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 munsigned 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 + 1unsigned long long z = a;z *= b;#ifdef _MSC_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x =(unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned 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/gconstexpr 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| <= blong 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| <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}// by [3]: |m0| <= b/g// by g != b: |m0| < b/gif (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) <= nn = (unsigned long long)(y_max / m);b = (unsigned long long)(y_max % m);std::swap(m, a);}return ans;}} // namespace internal} // namespace atcoder#line 5 "/home/seekworser/.cpp_lib/competitive_library/atcoder/internal_type_traits.hpp"namespace atcoder {namespace internal {#ifndef _MSC_VERtemplate <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;#elsetemplate <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;#endiftemplate <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 12 "/home/seekworser/.cpp_lib/competitive_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 internaltemplate <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 mint& rhs) { (*this)._v = rhs.val(); return *this; }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 mint& rhs) { (*this)._v = rhs.val(); return *this; }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 "/home/seekworser/.cpp_lib/competitive_library/competitive/math/modint.hpp"inline std::istream& operator>>(std::istream& is, atcoder::modint& x);inline std::istream& operator>>(std::istream& is, atcoder::modint998244353& x);inline std::istream& operator>>(std::istream& is, atcoder::modint1000000007& x);inline std::ostream& operator<<(std::ostream& os, const atcoder::modint& x);inline std::ostream& operator<<(std::ostream& os, const atcoder::modint998244353& x);inline std::ostream& operator<<(std::ostream& os, const atcoder::modint1000000007& x);inline std::istream& operator>>(std::istream& is, atcoder::modint& x) {ll a; is >> a; x = a; return is; }inline std::istream& operator>>(std::istream& is, atcoder::modint998244353& x) {ll a; is >> a; x = a; return is; }inline std::istream& operator>>(std::istream& is, atcoder::modint1000000007& x) {ll a; is >> a; x = a; return is; }inline std::ostream& operator<<(std::ostream& os, const atcoder::modint& x) { os << x.val(); return os; }inline std::ostream& operator<<(std::ostream& os, const atcoder::modint998244353& x) { os << x.val(); return os; }inline std::ostream& operator<<(std::ostream& os, const atcoder::modint1000000007& x) { os << x.val(); return os; }using modint998244353 = atcoder::modint998244353;using modint1000000007 = atcoder::modint1000000007;using modint = atcoder::modint;/*** @brief modint.hpp* @docs docs/math/modint.md*/#line 3 "/home/seekworser/.cpp_lib/competitive_library/competitive/std/io.hpp"// 演算子オーバーロード(プロトタイプ宣言)template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p);template <class T> inline istream& operator>>(istream& is, vector<T>& v);template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p);template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v);template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp);template <typename T> ostream &operator<<(ostream &os, const set<T> &st);template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st);template <typename T> ostream &operator<<(ostream &os, queue<T> q);template <typename T> ostream &operator<<(ostream &os, deque<T> q);template <typename T> ostream &operator<<(ostream &os, stack<T> st);template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq);// 演算子オーバーロードtemplate <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repe(x, v) is >> x; return is; }template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p) { os << p.first << " " << p.second; return os; }template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v) { rep(i, sz(v)) { os << v.at(i); if (i != sz(v) - 1) os << " "; }return os; }template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp) { for (auto &[key, val] : mp) { os << key << ":" << val << ""; } return os; }template <typename T> ostream &operator<<(ostream &os, const set<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os <<*itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os<< *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }template <typename T> ostream &operator<<(ostream &os, queue<T> q) { while (q.size()) { os << q.front() << " "; q.pop(); } return os; }template <typename T> ostream &operator<<(ostream &os, deque<T> q) { while (q.size()) { os << q.front() << " "; q.pop_front(); } return os; }template <typename T> ostream &operator<<(ostream &os, stack<T> st) { while (st.size()) { os << st.top() << " "; st.pop(); } return os; }template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq) { while (pq.size()) {os << pq.top() << " "; pq.pop(); } return os; }template <class T> inline vector<T>& operator--(vector<T>& v) { repe(x, v) --x; return v; }template <class T> inline vector<T>& operator++(vector<T>& v) { repe(x, v) ++x; return v; }template <typename T> void print_sep_end(string sep, string end, const T& val) { (void)sep; cout << val << end; };template <typename T1, typename... T2> void print_sep_end(string sep, string end, const T1 &val, const T2 &...remain) {cout << val << sep;print_sep_end(sep, end, remain...);};template <typename... T> void print(const T&...args) {print_sep_end(" ", "\n", args...);};#define debug(...) debug_func(0, #__VA_ARGS__, __VA_ARGS__) // debug print#ifdef LOCAL_TESTtemplate <typename T>void debug_func(int i, T name) { (void)i; (void)name; cerr << endl; }template <typename T1, typename T2, typename... T3> void debug_func(int i, const T1 &name, const T2 &a, const T3 &...b) {for ( ; name[i] != ',' && name[i] != '\0'; i++ ) cerr << name[i];cerr << ":" << a << " ";debug_func(i + 1, name, b...);}#endif#ifndef LOCAL_TESTtemplate <typename... T>void debug_func(const T &...) {}#endif/*** @brief io.hpp* @docs docs/std/io.md*/#line 6 "answer.cpp"int main() {using mint = modint998244353;ll h,w,k;cin >> h >> w >> k;Combination c(1000001, MODINT998244353);mint ans = 0;vl div = divisor(k);repe(p1, div) {ll p2 = k / p1;debug(p1, p2);if (p1 > h || p2 > w) continue;ans += mint(c(h, p1)) * mint(c(w, p2));}print(ans);}