From 8dbd7b2da0f9bfb22fcc39296e6054c569782ef1 Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Fri, 17 Feb 2023 16:18:41 +0800
Subject: [PATCH] =?UTF-8?q?#145.=20=E3=80=902020.11.30=20NOIP=E6=A8=A1?=
 =?UTF-8?q?=E6=8B=9F=E8=B5=9B=20T2=E3=80=91=E7=9F=A9=E9=98=B5=E6=B8=B8?=
 =?UTF-8?q?=E6=88=8F?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

https://sjzezoj.com/submission/70880
---
 S2OJ/145/145.cpp           | 68 ++++++++++++++++++++++++++++++++++++++
 S2OJ/145/data/matrix1.ans  |  3 ++
 S2OJ/145/data/matrix1.in   |  3 ++
 S2OJ/145/data/matrix10.ans |  3 ++
 S2OJ/145/data/matrix10.in  |  3 ++
 S2OJ/145/data/matrix11.ans |  3 ++
 S2OJ/145/data/matrix11.in  |  3 ++
 S2OJ/145/data/matrix12.ans |  3 ++
 S2OJ/145/data/matrix12.in  |  3 ++
 S2OJ/145/data/matrix13.ans |  3 ++
 S2OJ/145/data/matrix13.in  |  3 ++
 S2OJ/145/data/matrix14.ans |  3 ++
 S2OJ/145/data/matrix14.in  |  3 ++
 S2OJ/145/data/matrix15.ans |  3 ++
 S2OJ/145/data/matrix15.in  |  3 ++
 S2OJ/145/data/matrix16.ans |  3 ++
 S2OJ/145/data/matrix16.in  |  3 ++
 S2OJ/145/data/matrix17.ans |  3 ++
 S2OJ/145/data/matrix17.in  |  3 ++
 S2OJ/145/data/matrix18.ans |  3 ++
 S2OJ/145/data/matrix18.in  |  3 ++
 S2OJ/145/data/matrix19.ans |  3 ++
 S2OJ/145/data/matrix19.in  |  3 ++
 S2OJ/145/data/matrix2.ans  |  3 ++
 S2OJ/145/data/matrix2.in   |  3 ++
 S2OJ/145/data/matrix20.ans |  3 ++
 S2OJ/145/data/matrix20.in  |  3 ++
 S2OJ/145/data/matrix3.ans  |  3 ++
 S2OJ/145/data/matrix3.in   |  3 ++
 S2OJ/145/data/matrix4.ans  |  3 ++
 S2OJ/145/data/matrix4.in   |  3 ++
 S2OJ/145/data/matrix5.ans  |  3 ++
 S2OJ/145/data/matrix5.in   |  3 ++
 S2OJ/145/data/matrix6.ans  |  3 ++
 S2OJ/145/data/matrix6.in   |  3 ++
 S2OJ/145/data/matrix7.ans  |  3 ++
 S2OJ/145/data/matrix7.in   |  3 ++
 S2OJ/145/data/matrix8.ans  |  3 ++
 S2OJ/145/data/matrix8.in   |  3 ++
 S2OJ/145/data/matrix9.ans  |  3 ++
 S2OJ/145/data/matrix9.in   |  3 ++
 S2OJ/145/data/problem.conf |  3 ++
 42 files changed, 191 insertions(+)
 create mode 100644 S2OJ/145/145.cpp
 create mode 100644 S2OJ/145/data/matrix1.ans
 create mode 100644 S2OJ/145/data/matrix1.in
 create mode 100644 S2OJ/145/data/matrix10.ans
 create mode 100644 S2OJ/145/data/matrix10.in
 create mode 100644 S2OJ/145/data/matrix11.ans
 create mode 100644 S2OJ/145/data/matrix11.in
 create mode 100644 S2OJ/145/data/matrix12.ans
 create mode 100644 S2OJ/145/data/matrix12.in
 create mode 100644 S2OJ/145/data/matrix13.ans
 create mode 100644 S2OJ/145/data/matrix13.in
 create mode 100644 S2OJ/145/data/matrix14.ans
 create mode 100644 S2OJ/145/data/matrix14.in
 create mode 100644 S2OJ/145/data/matrix15.ans
 create mode 100644 S2OJ/145/data/matrix15.in
 create mode 100644 S2OJ/145/data/matrix16.ans
 create mode 100644 S2OJ/145/data/matrix16.in
 create mode 100644 S2OJ/145/data/matrix17.ans
 create mode 100644 S2OJ/145/data/matrix17.in
 create mode 100644 S2OJ/145/data/matrix18.ans
 create mode 100644 S2OJ/145/data/matrix18.in
 create mode 100644 S2OJ/145/data/matrix19.ans
 create mode 100644 S2OJ/145/data/matrix19.in
 create mode 100644 S2OJ/145/data/matrix2.ans
 create mode 100644 S2OJ/145/data/matrix2.in
 create mode 100644 S2OJ/145/data/matrix20.ans
 create mode 100644 S2OJ/145/data/matrix20.in
 create mode 100644 S2OJ/145/data/matrix3.ans
 create mode 100644 S2OJ/145/data/matrix3.in
 create mode 100644 S2OJ/145/data/matrix4.ans
 create mode 100644 S2OJ/145/data/matrix4.in
 create mode 100644 S2OJ/145/data/matrix5.ans
 create mode 100644 S2OJ/145/data/matrix5.in
 create mode 100644 S2OJ/145/data/matrix6.ans
 create mode 100644 S2OJ/145/data/matrix6.in
 create mode 100644 S2OJ/145/data/matrix7.ans
 create mode 100644 S2OJ/145/data/matrix7.in
 create mode 100644 S2OJ/145/data/matrix8.ans
 create mode 100644 S2OJ/145/data/matrix8.in
 create mode 100644 S2OJ/145/data/matrix9.ans
 create mode 100644 S2OJ/145/data/matrix9.in
 create mode 100644 S2OJ/145/data/problem.conf

diff --git a/S2OJ/145/145.cpp b/S2OJ/145/145.cpp
new file mode 100644
index 00000000..f2901dc0
--- /dev/null
+++ b/S2OJ/145/145.cpp
@@ -0,0 +1,68 @@
+#include <iostream>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 2e5 + 5;
+const int mod = 1e9 + 7;
+
+int inv[N], fac[N], inv_fac[N];
+
+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;
+    }
+
+    // ======
+
+    int t;
+
+    cin >> t;
+
+    while (t--) {
+        int n, m, k, res1 = 0, res2 = 0, res3 = 0, res4 = 0;
+
+        cin >> n >> m >> k;
+
+        for (int i = k & 1; i <= std::min(n, k); i += 2) {
+            res1 = (res1 + C(n, i)) % mod;
+        }
+
+        for (int i = k & 1; i <= std::min(m, k); i += 2) {
+            res2 = (res2 + C(m, i)) % mod;
+        }
+
+        if (n % 2 == 0 && m % 2 == 0) {
+            for (int i = std::max(n - k, 0); i <= std::min(n, k); i += 2) {
+                res3 = (res3 + C(n, i)) % mod;
+            }
+
+            for (int i = std::max(m - k, 0); i <= std::min(m, k); i += 2) {
+                res4 = (res4 + C(m, i)) % mod;
+            }
+        }
+
+        cout << ((static_cast<long long>(res1) * res2 % mod - static_cast<long long>(res3) * res4 % mod * inv[2] % mod) + mod) % mod << endl;
+    }
+
+    return 0;
+}
diff --git a/S2OJ/145/data/matrix1.ans b/S2OJ/145/data/matrix1.ans
new file mode 100644
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new file mode 100644
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diff --git a/S2OJ/145/data/matrix10.ans b/S2OJ/145/data/matrix10.ans
new file mode 100644
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