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S2OJ/1898/1898.cpp
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80
S2OJ/1898/1898.cpp
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#include <iostream>
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#include <algorithm>
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#include <iterator>
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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 = 2005;
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const int mod = 1e9 + 9;
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int n, k, inv[N], fac[N], inv_fac[N], a[N], b[N], l[N], f[N][N], g[N], ans;
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inline 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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cin >> n >> k;
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if ((n - k) % 2 == 1) {
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cout << 0 << endl;
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exit(0);
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}
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std::copy_n(std::istream_iterator<int>(cin), n, a + 1);
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std::copy_n(std::istream_iterator<int>(cin), n, b + 1);
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std::sort(a + 1, a + 1 + n);
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std::sort(b + 1, b + 1 + n);
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std::transform(a + 1, a + 1 + n, l + 1, [&](int x) {
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return std::distance(b + 1, std::lower_bound(b + 1, b + 1 + n, x));
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});
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f[0][0] = 1;
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for (int i = 1; i <= n; i++) {
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f[i][0] = f[i - 1][0];
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for (int j = 1; j <= i; j++) {
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f[i][j] = (static_cast<long long>(f[i - 1][j]) + static_cast<long long>(f[i - 1][j - 1]) * (l[i] - j + 1) % mod) % mod;
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}
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}
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for (int i = 0; i <= n; i++) {
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g[i] = static_cast<long long>(f[n][i]) * fac[n - i] % mod;
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}
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int w = (n + k) >> 1;
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for (int i = w; i <= n; i++) {
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if ((i - w) & 1) {
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ans = (static_cast<long long>(ans) - static_cast<long long>(C(i, w)) * g[i] % mod + mod) % mod;
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} else {
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ans = (static_cast<long long>(ans) + static_cast<long long>(C(i, w)) * g[i] % mod) % mod;
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}
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}
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cout << ans << endl;
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return 0;
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}
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