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- #include <bits/stdc++.h>
- using namespace std;
- const int N = 1e6 + 7, mod = 998244353;
- long long binexp(long long a, long long n) {
- long long res = 1;
- while(n) {
- if(n & 1) {
- res = (res * a) % mod;
- }
- n >>= 1;
- a = (a * a) % mod;
- }
- return res;
- }
- namespace ntt {
- long long w[N], k, nrev;
- inline void init(int n, int root) {
- w[0] = 1;
- k = binexp(root, (mod - 1) / n);
- nrev = binexp(n, mod - 2);
- for(int i = 1; i <= n; i++) {
- w[i] = (w[i - 1] * k) % mod;
- }
- }
- inline void ntt(vector<long long> &a, int n, bool inv = false) {
- a.resize(n);
- for(int i = 0, j = 0; i < n; i++) {
- if(i > j) swap(a[i], a[j]);
- for(int l = n / 2; (j ^= l) < l; l >>= 1);
- }
- for(int i = 2; i <= n; i <<= 1) {
- for(int j = 0; j < n; j += i) {
- for(int l = 0; l < i / 2; l++) {
- int x = j + l, y = j + l + (i / 2), z = (n / i) * l;
- long long tmp = (a[y] * w[(inv ? (n - z) : z)]) % mod;
- a[y] = (a[x] - tmp + mod) % mod;
- a[x] = (a[j + l] + tmp) % mod;
- }
- }
- }
- if(inv) {
- for(int i = 0; i < n; i++) {
- a[i] = (a[i] * nrev) % mod;
- }
- }
- }
- void multiply(vector<long long> &a, vector<long long> b, int root = 3) {
- int n = (int)a.size() + (int)b.size() - 1;
- while(n & (n - 1)) n++;
- a.resize(n);
- b.resize(n);
- init(n, root);
- ntt(a, n);
- ntt(b, n);
- for(int i = 0; i < n; i++) {
- a[i] = (a[i] * b[i]) % mod;
- }
- ntt(b, n, true);
- ntt(a, n, true);
- while(a.back() == 0) a.pop_back();
- }
- }
- int main() {
- ios_base::sync_with_stdio(false);
- cin.tie(nullptr);
- int n, m, s;
- cin >> n >> m >> s;
- // auto start = chrono::high_resolution_clock::now();
- vector<long long> v(m + 1, 1), ans(1, 1);
- while(n) {
- if(n & 1) {
- ntt::multiply(ans, v);
- if(ans.size() > s + 1) ans.resize(s + 1);
- }
- ntt::multiply(v, v);
- if(v.size() > s + 1) v.resize(s + 1);
- n >>= 1;
- }
- ans.resize(s + 1);
- cout << ans[s] << "\n";
- // auto stop = chrono::high_resolution_clock::now();
- // cerr << chrono::duration_cast<chrono::milliseconds>(stop - start).count() << "\n";
- return 0;
- }
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