From a97d1c11ac749925bb5f5c233ec9534a6440b288 Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Wed, 7 Dec 2022 16:16:54 +0800
Subject: [PATCH] E - BBQ Hard

https://atcoder.jp/contests/agc001/submissions/37074356
---
 AtCoder/AGC001/E/E.cpp              | 70 +++++++++++++++++++++++++++++
 AtCoder/AGC001/E/data/01-01.in      |  3 ++
 AtCoder/AGC001/E/data/01-01.out     |  3 ++
 AtCoder/AGC001/E/data/01-02.in      |  3 ++
 AtCoder/AGC001/E/data/01-02.out     |  3 ++
 AtCoder/AGC001/E/data/01-03.in      |  3 ++
 AtCoder/AGC001/E/data/01-03.out     |  3 ++
 AtCoder/AGC001/E/data/01-04.in      |  3 ++
 AtCoder/AGC001/E/data/01-04.out     |  3 ++
 AtCoder/AGC001/E/data/01-05.in      |  3 ++
 AtCoder/AGC001/E/data/01-05.out     |  3 ++
 AtCoder/AGC001/E/data/01-06.in      |  3 ++
 AtCoder/AGC001/E/data/01-06.out     |  3 ++
 AtCoder/AGC001/E/data/01-07.in      |  3 ++
 AtCoder/AGC001/E/data/01-07.out     |  3 ++
 AtCoder/AGC001/E/data/01-08.in      |  3 ++
 AtCoder/AGC001/E/data/01-08.out     |  3 ++
 AtCoder/AGC001/E/data/01-09.in      |  3 ++
 AtCoder/AGC001/E/data/01-09.out     |  3 ++
 AtCoder/AGC001/E/data/01-10.in      |  3 ++
 AtCoder/AGC001/E/data/01-10.out     |  3 ++
 AtCoder/AGC001/E/data/01-11.in      |  3 ++
 AtCoder/AGC001/E/data/01-11.out     |  3 ++
 AtCoder/AGC001/E/data/01-12.in      |  3 ++
 AtCoder/AGC001/E/data/01-12.out     |  3 ++
 AtCoder/AGC001/E/data/01-13.in      |  3 ++
 AtCoder/AGC001/E/data/01-13.out     |  3 ++
 AtCoder/AGC001/E/data/01-14.in      |  3 ++
 AtCoder/AGC001/E/data/01-14.out     |  3 ++
 AtCoder/AGC001/E/data/sample-01.in  |  3 ++
 AtCoder/AGC001/E/data/sample-01.out |  3 ++
 31 files changed, 160 insertions(+)
 create mode 100644 AtCoder/AGC001/E/E.cpp
 create mode 100644 AtCoder/AGC001/E/data/01-01.in
 create mode 100644 AtCoder/AGC001/E/data/01-01.out
 create mode 100644 AtCoder/AGC001/E/data/01-02.in
 create mode 100644 AtCoder/AGC001/E/data/01-02.out
 create mode 100644 AtCoder/AGC001/E/data/01-03.in
 create mode 100644 AtCoder/AGC001/E/data/01-03.out
 create mode 100644 AtCoder/AGC001/E/data/01-04.in
 create mode 100644 AtCoder/AGC001/E/data/01-04.out
 create mode 100644 AtCoder/AGC001/E/data/01-05.in
 create mode 100644 AtCoder/AGC001/E/data/01-05.out
 create mode 100644 AtCoder/AGC001/E/data/01-06.in
 create mode 100644 AtCoder/AGC001/E/data/01-06.out
 create mode 100644 AtCoder/AGC001/E/data/01-07.in
 create mode 100644 AtCoder/AGC001/E/data/01-07.out
 create mode 100644 AtCoder/AGC001/E/data/01-08.in
 create mode 100644 AtCoder/AGC001/E/data/01-08.out
 create mode 100644 AtCoder/AGC001/E/data/01-09.in
 create mode 100644 AtCoder/AGC001/E/data/01-09.out
 create mode 100644 AtCoder/AGC001/E/data/01-10.in
 create mode 100644 AtCoder/AGC001/E/data/01-10.out
 create mode 100644 AtCoder/AGC001/E/data/01-11.in
 create mode 100644 AtCoder/AGC001/E/data/01-11.out
 create mode 100644 AtCoder/AGC001/E/data/01-12.in
 create mode 100644 AtCoder/AGC001/E/data/01-12.out
 create mode 100644 AtCoder/AGC001/E/data/01-13.in
 create mode 100644 AtCoder/AGC001/E/data/01-13.out
 create mode 100644 AtCoder/AGC001/E/data/01-14.in
 create mode 100644 AtCoder/AGC001/E/data/01-14.out
 create mode 100644 AtCoder/AGC001/E/data/sample-01.in
 create mode 100644 AtCoder/AGC001/E/data/sample-01.out

diff --git a/AtCoder/AGC001/E/E.cpp b/AtCoder/AGC001/E/E.cpp
new file mode 100644
index 00000000..e6381854
--- /dev/null
+++ b/AtCoder/AGC001/E/E.cpp
@@ -0,0 +1,70 @@
+#include <iostream>
+#include <algorithm>
+#include <cstring>
+#include <iterator>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 2e5 + 5,
+          M = 2005;
+const int mod = 1e9 + 7;
+
+int n, m, a[N], b[N], inv[M << 2], fac[M << 2], inv_fac[M << 2], _f[M << 1][M << 1], *_pf[M << 1], **f, 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 < M << 2; i++) {
+        fac[i] = static_cast<long long>(fac[i - 1]) * i % mod;
+    }
+
+    inv[0] = inv[1] = 1;
+    for (int i = 2; i < M << 2; 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 < M << 2; i++) {
+        inv_fac[i] = static_cast<long long>(inv_fac[i - 1]) * inv[i] % mod;
+    }
+
+    for (int i = 0; i < M << 1; i++) {
+        _pf[i] = _f[i] + M;
+    }
+
+    f = _pf + M;
+
+    cin >> n;
+
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i] >> b[i];
+
+        f[-a[i]][-b[i]]++;
+    }
+
+    for (int i = -2000; i <= 2000; i++) {
+        for (int j = -2000; j <= 2000; j++) {
+            f[i][j] = (static_cast<long long>(f[i][j]) + f[i - 1][j] + f[i][j - 1]) % mod;
+        }
+    }
+
+    for (int i = 1; i <= n; i++) {
+        ans = (static_cast<long long>(ans) + f[a[i]][b[i]]) % mod;
+    }
+
+    for (int i = 1; i <= n; i++) {
+        ans = ((static_cast<long long>(ans) - C(2 * a[i] + 2 * b[i], 2 * a[i])) % mod + mod) % mod;
+    }
+
+    cout << (static_cast<long long>(ans) * inv[2] % mod) << endl;
+
+    return 0;
+}
diff --git a/AtCoder/AGC001/E/data/01-01.in b/AtCoder/AGC001/E/data/01-01.in
new file mode 100644
index 00000000..ae5e2e5f
--- /dev/null
+++ b/AtCoder/AGC001/E/data/01-01.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
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+size 20
diff --git a/AtCoder/AGC001/E/data/01-01.out b/AtCoder/AGC001/E/data/01-01.out
new file mode 100644
index 00000000..4cbe1c26
--- /dev/null
+++ b/AtCoder/AGC001/E/data/01-01.out
@@ -0,0 +1,3 @@
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diff --git a/AtCoder/AGC001/E/data/01-02.in b/AtCoder/AGC001/E/data/01-02.in
new file mode 100644
index 00000000..fecb1580
--- /dev/null
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diff --git a/AtCoder/AGC001/E/data/01-02.out b/AtCoder/AGC001/E/data/01-02.out
new file mode 100644
index 00000000..01e58a21
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new file mode 100644
index 00000000..5a7edd0a
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diff --git a/AtCoder/AGC001/E/data/01-03.out b/AtCoder/AGC001/E/data/01-03.out
new file mode 100644
index 00000000..fcea1e94
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new file mode 100644
index 00000000..2f4625dc
--- /dev/null
+++ b/AtCoder/AGC001/E/data/01-04.in
@@ -0,0 +1,3 @@
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diff --git a/AtCoder/AGC001/E/data/01-04.out b/AtCoder/AGC001/E/data/01-04.out
new file mode 100644
index 00000000..15a59c93
--- /dev/null
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new file mode 100644
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new file mode 100644
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new file mode 100644
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new file mode 100644
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new file mode 100644
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new file mode 100644
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new file mode 100644
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new file mode 100644
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