From 941e72c53ec854755aed24a2c7b966b551a133ff Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Wed, 8 Feb 2023 08:50:20 +0800
Subject: [PATCH] =?UTF-8?q?#1898.=20=E3=80=90BZOJ3622=E3=80=91=E5=B7=B2?=
 =?UTF-8?q?=E7=BB=8F=E6=B2=A1=E6=9C=89=E4=BB=80=E4=B9=88=E5=A5=BD=E5=AE=B3?=
 =?UTF-8?q?=E6=80=95=E7=9A=84=E4=BA=86?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

https://sjzezoj.com/submission/68532
---
 S2OJ/1898/1898.cpp          | 80 +++++++++++++++++++++++++++++++++++++
 S2OJ/1898/data/data1.in     |  3 ++
 S2OJ/1898/data/data1.out    |  3 ++
 S2OJ/1898/data/data10.in    |  3 ++
 S2OJ/1898/data/data10.out   |  3 ++
 S2OJ/1898/data/data2.in     |  3 ++
 S2OJ/1898/data/data2.out    |  3 ++
 S2OJ/1898/data/data3.in     |  3 ++
 S2OJ/1898/data/data3.out    |  3 ++
 S2OJ/1898/data/data4.in     |  3 ++
 S2OJ/1898/data/data4.out    |  3 ++
 S2OJ/1898/data/data5.in     |  3 ++
 S2OJ/1898/data/data5.out    |  3 ++
 S2OJ/1898/data/data6.in     |  3 ++
 S2OJ/1898/data/data6.out    |  3 ++
 S2OJ/1898/data/data7.in     |  3 ++
 S2OJ/1898/data/data7.out    |  3 ++
 S2OJ/1898/data/data8.in     |  3 ++
 S2OJ/1898/data/data8.out    |  3 ++
 S2OJ/1898/data/data9.in     |  3 ++
 S2OJ/1898/data/data9.out    |  3 ++
 S2OJ/1898/data/problem.conf |  3 ++
 22 files changed, 143 insertions(+)
 create mode 100644 S2OJ/1898/1898.cpp
 create mode 100644 S2OJ/1898/data/data1.in
 create mode 100644 S2OJ/1898/data/data1.out
 create mode 100644 S2OJ/1898/data/data10.in
 create mode 100644 S2OJ/1898/data/data10.out
 create mode 100644 S2OJ/1898/data/data2.in
 create mode 100644 S2OJ/1898/data/data2.out
 create mode 100644 S2OJ/1898/data/data3.in
 create mode 100644 S2OJ/1898/data/data3.out
 create mode 100644 S2OJ/1898/data/data4.in
 create mode 100644 S2OJ/1898/data/data4.out
 create mode 100644 S2OJ/1898/data/data5.in
 create mode 100644 S2OJ/1898/data/data5.out
 create mode 100644 S2OJ/1898/data/data6.in
 create mode 100644 S2OJ/1898/data/data6.out
 create mode 100644 S2OJ/1898/data/data7.in
 create mode 100644 S2OJ/1898/data/data7.out
 create mode 100644 S2OJ/1898/data/data8.in
 create mode 100644 S2OJ/1898/data/data8.out
 create mode 100644 S2OJ/1898/data/data9.in
 create mode 100644 S2OJ/1898/data/data9.out
 create mode 100644 S2OJ/1898/data/problem.conf

diff --git a/S2OJ/1898/1898.cpp b/S2OJ/1898/1898.cpp
new file mode 100644
index 00000000..98be5b1e
--- /dev/null
+++ b/S2OJ/1898/1898.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;
+}
diff --git a/S2OJ/1898/data/data1.in b/S2OJ/1898/data/data1.in
new file mode 100644
index 00000000..3e1af26c
--- /dev/null
+++ b/S2OJ/1898/data/data1.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bf2a7baff49e587def237afa7246dfa980296d4b7a2ac2741ba30addb3a3c724
+size 27555
diff --git a/S2OJ/1898/data/data1.out b/S2OJ/1898/data/data1.out
new file mode 100644
index 00000000..80f7c8b8
--- /dev/null
+++ b/S2OJ/1898/data/data1.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:17dc755c5a224a0f898091ecc38d24ef19f3f19f4918ba1f906a911cceab1150
+size 10
diff --git a/S2OJ/1898/data/data10.in b/S2OJ/1898/data/data10.in
new file mode 100644
index 00000000..521c198c
--- /dev/null
+++ b/S2OJ/1898/data/data10.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2a7b0af3edde0558a50ff5ee95c164691aee0a63e031188ca2b85f18e8ba02d8
+size 27570
diff --git a/S2OJ/1898/data/data10.out b/S2OJ/1898/data/data10.out
new file mode 100644
index 00000000..394ef510
--- /dev/null
+++ b/S2OJ/1898/data/data10.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:53e54a5a99721bcdef4366426de890a96127b217c25543e3ef5e8fcef5a37144
+size 10
diff --git a/S2OJ/1898/data/data2.in b/S2OJ/1898/data/data2.in
new file mode 100644
index 00000000..ca97ecb4
--- /dev/null
+++ b/S2OJ/1898/data/data2.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:63715fca85ed323c8686e1a8eca31c72de2c1b9b4503223d098e5be58e7b42bb
+size 2761
diff --git a/S2OJ/1898/data/data2.out b/S2OJ/1898/data/data2.out
new file mode 100644
index 00000000..35e75fec
--- /dev/null
+++ b/S2OJ/1898/data/data2.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2382d33bb3545a4ad3a0ba17b7216aa3cb81b1bfc9b0b425c851a19b5536931f
+size 10
diff --git a/S2OJ/1898/data/data3.in b/S2OJ/1898/data/data3.in
new file mode 100644
index 00000000..c8274d35
--- /dev/null
+++ b/S2OJ/1898/data/data3.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4bb490429c7ea86341b074ee2c8b0f3f91441aa050875e95c9d29e244fc37269
+size 1381
diff --git a/S2OJ/1898/data/data3.out b/S2OJ/1898/data/data3.out
new file mode 100644
index 00000000..2f794e45
--- /dev/null
+++ b/S2OJ/1898/data/data3.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d22547682891733166e878dceff46acd77b3e8dd9883ff508cbab772b890f73b
+size 10
diff --git a/S2OJ/1898/data/data4.in b/S2OJ/1898/data/data4.in
new file mode 100644
index 00000000..59c6880d
--- /dev/null
+++ b/S2OJ/1898/data/data4.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:20770e7dbd5d8ab31e2185a1d3fcf3639ef4dcdfa4298c1c5e9bde4c42948088
+size 27543
diff --git a/S2OJ/1898/data/data4.out b/S2OJ/1898/data/data4.out
new file mode 100644
index 00000000..0ae7f33c
--- /dev/null
+++ b/S2OJ/1898/data/data4.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c8fa3c46ba4e9e09dcc99fcb0533162f6d7bd1af64e0cc133de1219019aa6d5b
+size 9
diff --git a/S2OJ/1898/data/data5.in b/S2OJ/1898/data/data5.in
new file mode 100644
index 00000000..a66c0177
--- /dev/null
+++ b/S2OJ/1898/data/data5.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3051dd96bb1847824d690a49865bf50c2faf27ed7e142e65ec0999c3900624e0
+size 27522
diff --git a/S2OJ/1898/data/data5.out b/S2OJ/1898/data/data5.out
new file mode 100644
index 00000000..d4d395d2
--- /dev/null
+++ b/S2OJ/1898/data/data5.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5d51530d86a45ab89b877d9a60703a8b43dcad00ec6a9099fbbfa0188a294db5
+size 10
diff --git a/S2OJ/1898/data/data6.in b/S2OJ/1898/data/data6.in
new file mode 100644
index 00000000..34cd0bc6
--- /dev/null
+++ b/S2OJ/1898/data/data6.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fd3eb462e3c46613d8237930c8faa7a58b6d1407946b1189e04a5d193c5b82cf
+size 202
diff --git a/S2OJ/1898/data/data6.out b/S2OJ/1898/data/data6.out
new file mode 100644
index 00000000..2282bfe6
--- /dev/null
+++ b/S2OJ/1898/data/data6.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:11b97ca37e6fa8083cff17d690ef686be16876caf6ab1e059df0277a3df19d05
+size 6
diff --git a/S2OJ/1898/data/data7.in b/S2OJ/1898/data/data7.in
new file mode 100644
index 00000000..12985462
--- /dev/null
+++ b/S2OJ/1898/data/data7.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d558bf692af5c0344b692dc8663060c35a81cd200a6abaa712a3873e0e9eefe9
+size 27562
diff --git a/S2OJ/1898/data/data7.out b/S2OJ/1898/data/data7.out
new file mode 100644
index 00000000..b8227cdb
--- /dev/null
+++ b/S2OJ/1898/data/data7.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:681e479adee0ce36b2c076df45750bacb56dd5d411be0f61ececabeb3facbeea
+size 9
diff --git a/S2OJ/1898/data/data8.in b/S2OJ/1898/data/data8.in
new file mode 100644
index 00000000..fd1d9c86
--- /dev/null
+++ b/S2OJ/1898/data/data8.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d68b61860e828991f09aeb68db116bb916b976abf2ddb5ccaaadb7cec24a62b7
+size 2766
diff --git a/S2OJ/1898/data/data8.out b/S2OJ/1898/data/data8.out
new file mode 100644
index 00000000..6cdd35d9
--- /dev/null
+++ b/S2OJ/1898/data/data8.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9d3c89bc45c917e0ef1677009dcc822bdd96b70ae90ba2550d99d3ec8b957fb7
+size 10
diff --git a/S2OJ/1898/data/data9.in b/S2OJ/1898/data/data9.in
new file mode 100644
index 00000000..41cbbe05
--- /dev/null
+++ b/S2OJ/1898/data/data9.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b039deaed8891389c23f00429841bdbf8e7829fa1698739b4ac58d9fcbe93728
+size 27568
diff --git a/S2OJ/1898/data/data9.out b/S2OJ/1898/data/data9.out
new file mode 100644
index 00000000..818790ab
--- /dev/null
+++ b/S2OJ/1898/data/data9.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6126bde8bed85482fa0d451178491a93bc7417f7291cc8c907d517c8337a51a4
+size 10
diff --git a/S2OJ/1898/data/problem.conf b/S2OJ/1898/data/problem.conf
new file mode 100644
index 00000000..bfa99af8
--- /dev/null
+++ b/S2OJ/1898/data/problem.conf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:14af6f937e7343ed6065b7f1ae40f21cb514266e9af9ad52c51237646b759e35
+size 208