結果

問題 No.1388 Less than K
ユーザー PCTprobability
提出日時 2021-02-07 23:06:56
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 941 ms / 3,000 ms
コード長 32,841 bytes
コンパイル時間 4,385 ms
コンパイル使用メモリ 244,176 KB
最終ジャッジ日時 2025-01-18 15:46:15
ジャッジサーバーID
（参考情報） 		judge2 / judge2
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ファイルパターン 結果
sample AC * 3
other AC * 74
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ソースコード

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プレゼンテーションモードにする

#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 = 500000) 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(500000);
  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 = 3000000;
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;
}
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