#include using namespace std; #ifdef DEBUG int __lg(int n){ return 31 - __builtin_clz(n); } #endif template vector operator-(vector a) { for (auto&& e : a) e = -e; return a; } template vector& operator+=(vector& a, const vector& b) { a.resize(max(a.size(), b.size())); for (int i = 0; i < (int)b.size(); ++i) a[i] += b[i]; return a; } template vector operator+(vector a, const vector& b) { return a += b; } template vector& operator-=(vector& a, const vector& b) { a.resize(max(a.size(), b.size())); for (int i = 0; i < (int)b.size(); ++i) a[i] -= b[i]; return a; } template vector operator-(vector a, const vector& b) { return a -= b; } template vector& operator<<=(vector& a, size_t n) { return a.insert(begin(a), n, 0), a; } template vector operator<<(vector a, size_t n) { return a <<= n; } template vector& operator>>=(vector& a, size_t n) { return a.erase(begin(a), begin(a) + min(a.size(), n)), a; } template vector operator>>(vector a, size_t n) { return a >>= n; } template vector operator*(const vector& a, const vector& b) { if (a.empty() or b.empty()) return {}; vector res(a.size() + b.size() - 1); for (int i = 0; i < (int)a.size(); ++i) for (int j = 0; j < (int)b.size(); ++j) res[i + j] += a[i] * b[j]; return res; } template vector& operator*=(vector& a, const vector& b) { return a = a * b; } template vector inverse(const vector& a) { assert(not a.empty() and not (a[0] == 0)); vector b{1 / a[0]}; while (b.size() < a.size()) { vector x(begin(a), begin(a) + min(a.size(), 2 * b.size())); x *= b * b; b.resize(2 * b.size()); for (auto i = b.size() / 2; i < min(x.size(), b.size()); ++i) b[i] = -x[i]; } return {begin(b), begin(b) + a.size()}; } template vector operator/(vector a, vector b) { if (a.size() < b.size()) return {}; reverse(begin(a), end(a)), reverse(begin(b), end(b)); int n = a.size() - b.size() + 1; a.resize(n), b.resize(n); a *= inverse(b); return {rend(a) - n, rend(a)}; } template vector& operator/=(vector& a, const vector& b) { return a = a / b; } template vector operator%(vector a, const vector& b) { if (a.size() < b.size()) return a; a -= a / b * b; return {begin(a), begin(a) + (b.size() - 1)}; } template vector& operator%=(vector& a, const vector& b) { return a = a % b; } template vector derivative(const vector& a) { vector res(max((int)a.size() - 1, 0)); for (int i = 0; i < (int)res.size(); ++i) res[i] = (i + 1) * a[i + 1]; return res; } template vector primitive(const vector& a) { vector res(a.size() + 1); for (int i = 1; i < (int)res.size(); ++i) res[i] = a[i - 1] / i; return res; } template vector logarithm(const vector& a) { assert(not a.empty() and a[0] == 1); auto res = primitive(derivative(a) * inverse(a)); return {begin(res), begin(res) + a.size()}; } template vector exponent(const vector& a) { assert(a.empty() or a[0] == 0); vector b{1}; while (b.size() < a.size()) { vector x(begin(a), begin(a) + min(a.size(), 2 * b.size())); x[0] += 1; b.resize(2 * b.size()); x -= logarithm(b); x *= {begin(b), begin(b) + b.size() / 2}; for (auto i = b.size() / 2; i < min(x.size(), b.size()); ++i) b[i] = x[i]; } return {begin(b), begin(b) + a.size()}; } template > constexpr T power(T a, long long n, Op op = Op(), T e = {1}) { assert(n >= 0); while (n) { if (n & 1) e = op(e, a); if (n >>= 1) a = op(a, a); } return e; } template void ntt(vector& a, bool inverse) { int n = size(a); assert((n & (n - 1)) == 0); if (n < 2) return; assert((T::mod - 1) % n == 0); static vector w{1}, iw{1}; for (int m = size(w); m < n / 2; m *= 2) { static T root = 2; while (power(root, (T::mod - 1) / 2) == 1) root += 1; T dw = power(root, (T::mod - 1) / (4 * m)), idw = 1 / dw; w.resize(2 * m), iw.resize(2 * m); for (int i = 0; i < m; ++i) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * idw; } if (not inverse) { for (int m = n; m >>= 1; ) { for (int s = 0, k = 0; s < n; s += 2 * m, ++k) { for (int i = s, j = s + m; i < s + m; ++i, ++j) { T x = a[i], y = a[j] * w[k]; a[i] = x + y, a[j] = x - y; } } } } else { for (int m = 1; m < n; m *= 2) { for (int s = 0, k = 0; s < n; s += 2 * m, ++k) { for (int i = s, j = s + m; i < s + m; ++i, ++j) { T x = a[i], y = a[j]; a[i] = x + y, a[j] = (x - y) * iw[k]; } } } auto inv = 1 / T(n); for (auto&& e : a) e *= inv; } } template struct montgomery { using m = montgomery; static constexpr unsigned mod = M, neg_inv = [] { static_assert(mod < 1 << 30 and mod & 1); auto inv = mod; while (mod * inv != 1) inv *= 2 - mod * inv; return -inv; }(), sq = -(uint64_t)mod % mod; static unsigned reduce(uint64_t x) { return (x + (uint64_t)mod * ((unsigned)x * neg_inv)) >> 32; } unsigned v; montgomery() : v(0) {} montgomery(long long x) { if ((x %= mod) < 0) x += mod; v = reduce((uint64_t)x * sq); } int get() const { auto res = reduce(v); return res < mod ? res : res - mod; } m operator-() const { return m() -= *this; } m& operator+=(m b) { if ((int)(v += b.v - 2 * mod) < 0) v += 2 * mod; return *this; } m& operator-=(m b) { if ((int)(v -= b.v) < 0) v += 2 * mod; return *this; } m& operator*=(m b) { v = reduce((uint64_t)v * b.v); return *this; } m& operator/=(m b) { return *this *= power(b, mod - 2); } friend m operator+(m a, m b) { return a += b; } friend m operator-(m a, m b) { return a -= b; } friend m operator*(m a, m b) { return a *= b; } friend m operator/(m a, m b) { return a /= b; } friend bool operator==(m a, m b) { return a.v == b.v; } }; using mint = montgomery<998244353>; vector fact, inv_fact, minv; void prepare(int n) { fact.resize(n + 1), inv_fact.resize(n + 1), minv.resize(n + 1); for (int i = 0; i <= n; ++i) fact[i] = i ? fact[i - 1] * i : 1; inv_fact[n] = power(fact[n], mint::mod - 2); for (int i = n; i--; ) inv_fact[i] = (i + 1) * inv_fact[i + 1]; for (int i = 1; i <= n; ++i) minv[i] = inv_fact[i] * fact[i - 1]; } mint binom(int n, int k) { if (k < 0 or k > n) return 0; return fact[n] * inv_fact[k] * inv_fact[n - k]; } template <> mint& mint::operator/=(mint b) { return *this *= b.v < minv.size() ? minv[b.v] : power(b, mod - 2); } struct dual_vec { vector v; void resize(int sz) { v.resize(sz); } }; dual_vec mfft(const vector& a, int sz) { dual_vec fa{a}; fa.resize(sz), ntt(fa.v, false); return fa; } dual_vec operator*(dual_vec a, const dual_vec& b) { for (int i = 0; i < (int)a.v.size(); ++i) a.v[i] *= b.v[i]; return a; } vector ifft(dual_vec fa, int n) { ntt(fa.v, true), fa.resize(n); return fa.v; } vector operator*(const vector& a, const vector& b) { if (a.empty() or b.empty()) return {}; int n = a.size(), m = b.size(), sz = 1 << __lg(2 * (n + m - 1) - 1); if (min(n, m) < 30) { vector c(n + m - 1); for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) c[i + j] += a[i] * b[j]; return c; } if (a == b) { dual_vec fl = mfft(a, sz); return ifft(fl * fl, n + m - 1); } return ifft(mfft(a, sz) * mfft(b, sz), n + m - 1); } vector inverse(const vector& a) { assert(not a.empty() and not (a[0] == 0)); vector b{1 / a[0]}; for (int m = 1; m < (int)a.size(); m *= 2) { vector x(begin(a), begin(a) + min(a.size(), 2 * m)); dual_vec fb = mfft(b, 2 * m); x = ifft(mfft(x, 2 * m) * fb, 2 * m); fill(begin(x), begin(x) + m, 0); x = -ifft(mfft(x, 2 * m) * fb, 2 * m); b.insert(end(b), begin(x) + m, end(x)); } return {begin(b), begin(b) + a.size()}; } vector exponent(const vector& a) { assert(a.empty() or a[0] == 0); vector b{1, 1 < a.size() ? a[1] : 0}, c{1}; dual_vec half_fc = mfft(c, 1), fc = mfft(c, 2); for (int m = 2; m < (int)a.size(); m *= 2) { dual_vec fb = mfft(b, 2 * m), half_fb = fb; half_fb.resize(m); half_fc = fc; vector z = ifft(half_fb * half_fc, m); fill(begin(z), begin(z) + m / 2, 0); z = -ifft(mfft(z, m) * half_fc, m); c.insert(end(c), begin(z) + m / 2, end(z)); fc = mfft(c, 2 * m); vector x(begin(a), begin(a) + min(a.size(), m)); x = derivative(x), x.push_back(0); dual_vec fx = mfft(x, m); x = ifft(fx * half_fb, m); x -= derivative(b); x.resize(2 * m); for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = 0; x = ifft(mfft(x, 2 * m) * fc, 2 * m); x = primitive(x), x.pop_back(); for (int i = m; i < min(a.size(), 2 * m); ++i) x[i] += a[i]; fill(begin(x), begin(x) + m, 0); x = ifft(mfft(x, 2 * m) * fb, 2 * m); b.insert(end(b), begin(x) + m, end(x)); } return {begin(b), begin(b) + a.size()}; } vector power(vector a, long long m) { int n = size(a), tz = 0; while (tz < n and a[tz] == 0) ++tz; if (n == 0 or (tz and m >= (n + tz - 1) / tz)) return vector(n); a >>= tz; auto a0 = a[0]; a *= vector{1 / a0}; a = exponent(logarithm(a) * vector{m}); a *= vector{power(a0, m)}; return a <<= tz * m; } vector resize(vector a, int sz) { a.resize(sz); return a; } int main(){ int N, M, K; cin >> N >> M >> K; if(M == K) M--; if(M == 0)return puts("0") & 0; vector F(M * 2 + 1); mint s = 0; for(int i = -M; i <= M; i++) if(i != K && i != -K){ F[i + M] = 1; s += 1; } vector S(M + 1); S[M] = s; auto Q = vector{1, -1} * (F - S) * (F - S); F.resize(N * M); auto P = power(F, N + 2); Q.resize(N * M); cout << (P * inverse(Q))[M * N - 1].get() << endl; }