// #pragma GCC target("avx2") #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") #include using namespace std; using P = pair; const int M = 998244353; long long powmod(long long a, long long b) { long long res = 1; while (b) { if (b & 1) { res = res * a % M; } b >>= 1; a = a * a % M; } return res; } long long inv(long long a) { return powmod(a, M - 2); } int blim = 2048; vector> binom_small(blim, vector(blim)); long long binom(int n, int r) { if (n - r < r) r = n - r; if (n < 0 || r < 0 || n < r) return 0; if (n < blim) return binom_small[n][r]; long long u = 1, d = 1; for (int i = 0; i < r; ++i) { u = u * (n - i) % M; d = d * (i + 1) % M; } return u * inv(d) % M; } int main() { cin.tie(0); ios::sync_with_stdio(0); for (int i = 0; i < blim; ++i) { binom_small[i][0] = binom_small[i][i] = 1; for (int j = 1; j < i; ++j) { binom_small[i][j] = (binom_small[i - 1][j - 1] + binom_small[i - 1][j]) % M; } } int n, m, k; cin >> n >> m >> k; vector> dp1(m + 3, vector(m + 3)); dp1[0][1] = 1; for (int i = 1; i < m + 3; ++i) { vector imos(m + 4); for (int j = 0; j < m + 3; ++j) { imos[j + 1] = (imos[j] + dp1[i - 1][j]) % M; } for (int j = 1; j < m + 3; ++j) { dp1[i][j] = (imos[j] - imos[(j + 1) / 2] + M) % M; } } vector x(m + 3); for (int i = 0; i < m + 3 && i <= n; ++i) { long long b = binom(n, i); for (int j = 0; j + 1 < m + 3; ++j) { x[j] = (x[j] + dp1[i][j + 1] * b) % M; } } vector> dp2(13, vector(m + 3)); dp2[0][1] = 1; for (int i = 0; i + 1 < 13; ++i) { for (int j = 1; j < m + 3; ++j) { for (int l = 2; j * l < m + 3; ++l) { dp2[i + 1][j * l] = (dp2[i + 1][j * l] + dp2[i][j] * x[l - 1]) % M; } } } long long ans = 0; for (int i = 0; i < 13; ++i) { long long p = binom(k, i); for (int j = 0; j <= m; ++j) { ans = (ans + dp2[i][j] * p) % M; } } cout << ans << '\n'; return 0; }