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68
Luogu/P5857/P5857.cpp
Normal file
68
Luogu/P5857/P5857.cpp
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#include <iostream>
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using std::cin;
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using std::cout;
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const char endl = '\n';
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const int N = 2e5 + 5;
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const int mod = 998244353;
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int inv[N], fac[N], inv_fac[N];
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int C(int n, int m) {
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return static_cast<long long>(fac[n]) * inv_fac[m] % mod * inv_fac[n - m] % mod;
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}
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int main() {
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std::ios::sync_with_stdio(false);
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cin.tie(nullptr);
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fac[0] = 1;
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for (int i = 1; i < N; i++) {
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fac[i] = static_cast<long long>(fac[i - 1]) * i % mod;
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}
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inv[0] = inv[1] = 1;
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for (int i = 2; i < N; i++) {
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inv[i] = static_cast<long long>(mod - (mod / i)) * inv[mod % i] % mod;
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}
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inv_fac[0] = inv_fac[1] = 1;
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for (int i = 2; i < N; i++) {
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inv_fac[i] = static_cast<long long>(inv_fac[i - 1]) * inv[i] % mod;
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}
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// ======
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int t;
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cin >> t;
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while (t--) {
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int n, m, k, res1 = 0, res2 = 0, res3 = 0, res4 = 0;
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cin >> n >> m >> k;
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for (int i = k & 1; i <= std::min(n, k); i += 2) {
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res1 = (res1 + C(n, i)) % mod;
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}
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for (int i = k & 1; i <= std::min(m, k); i += 2) {
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res2 = (res2 + C(m, i)) % mod;
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}
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if (n % 2 == 0 && m % 2 == 0) {
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for (int i = std::max(n - k, 0); i <= std::min(n, k); i += 2) {
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res3 = (res3 + C(n, i)) % mod;
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}
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for (int i = std::max(m - k, 0); i <= std::min(m, k); i += 2) {
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res4 = (res4 + C(m, i)) % mod;
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}
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}
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cout << ((static_cast<long long>(res1) * res2 % mod - static_cast<long long>(res3) * res4 % mod * inv[2] % mod) + mod) % mod << endl;
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}
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return 0;
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}
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