From 09e9e78b0840be9b2cc244af890b58f58a9d87bc Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Wed, 8 Feb 2023 08:48:33 +0800
Subject: [PATCH] =?UTF-8?q?P4859=20=E5=B7=B2=E7=BB=8F=E6=B2=A1=E6=9C=89?=
 =?UTF-8?q?=E4=BB=80=E4=B9=88=E5=A5=BD=E5=AE=B3=E6=80=95=E7=9A=84=E4=BA=86?=
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https://www.luogu.com.cn/record/101676924
---
 Luogu/P4859/P4859.cpp | 80 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)
 create mode 100644 Luogu/P4859/P4859.cpp

diff --git a/Luogu/P4859/P4859.cpp b/Luogu/P4859/P4859.cpp
new file mode 100644
index 00000000..98be5b1e
--- /dev/null
+++ b/Luogu/P4859/P4859.cpp
@@ -0,0 +1,80 @@
+#include <iostream>
+#include <algorithm>
+#include <iterator>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 2005;
+const int mod = 1e9 + 9;
+
+int n, k, inv[N], fac[N], inv_fac[N], a[N], b[N], l[N], f[N][N], g[N], ans;
+
+inline int C(int n, int m) {
+    return static_cast<long long>(fac[n]) * inv_fac[m] % mod * inv_fac[n - m] % mod;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    fac[0] = 1;
+    for (int i = 1; i < N; i++) {
+        fac[i] = static_cast<long long>(fac[i - 1]) * i % mod;
+    }
+
+    inv[0] = inv[1] = 1;
+    for (int i = 2; i < N; i++) {
+        inv[i] = static_cast<long long>(mod - (mod / i)) * inv[mod % i] % mod;
+    }
+
+    inv_fac[0] = inv_fac[1] = 1;
+    for (int i = 2; i < N; i++) {
+        inv_fac[i] = static_cast<long long>(inv_fac[i - 1]) * inv[i] % mod;
+    }
+
+    cin >> n >> k;
+
+    if ((n - k) % 2 == 1) {
+        cout << 0 << endl;
+
+        exit(0);
+    }
+
+    std::copy_n(std::istream_iterator<int>(cin), n, a + 1);
+    std::copy_n(std::istream_iterator<int>(cin), n, b + 1);
+
+    std::sort(a + 1, a + 1 + n);
+    std::sort(b + 1, b + 1 + n);
+    std::transform(a + 1, a + 1 + n, l + 1, [&](int x) {
+        return std::distance(b + 1, std::lower_bound(b + 1, b + 1 + n, x));
+    });
+
+    f[0][0] = 1;
+
+    for (int i = 1; i <= n; i++) {
+        f[i][0] = f[i - 1][0];
+
+        for (int j = 1; j <= i; j++) {
+            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;
+        }
+    }
+
+    for (int i = 0; i <= n; i++) {
+        g[i] = static_cast<long long>(f[n][i]) * fac[n - i] % mod;
+    }
+
+    int w = (n + k) >> 1;
+    for (int i = w; i <= n; i++) {
+        if ((i - w) & 1) {
+            ans = (static_cast<long long>(ans) - static_cast<long long>(C(i, w)) * g[i] % mod + mod) % mod;
+        } else {
+            ans = (static_cast<long long>(ans) + static_cast<long long>(C(i, w)) * g[i] % mod) % mod;
+        }
+    }
+
+    cout << ans << endl;
+
+    return 0;
+}