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usaco/gold/mooroutes/main.cpp

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+#include <iostream>
+#define ll long long
+using namespace std;
+
+const int A = 1e6+1;
+const int M = 1e9+7;
+const int N = 1e5;
+ll factorials[A];
+ll inv_factorials[A];
+ll modules[N];
+
+ll exp(ll x, ll n) {
+    x %= M;
+    ll res = 1;
+    while (n > 0) {
+        if (n % 2 == 1) { res = res * x % M; }
+        x = x * x % M;
+        n /= 2;
+    }
+    return res;
+}
+
+ll C(ll n, ll k) {
+    return factorials[n] * inv_factorials[n - k] % M * inv_factorials[k] % M;
+}
+
+int main() {
+    int n;
+    cin >> n;
+    for(int i = 0; i < n; i++) {
+        cin >> modules[i];
+        modules[i] /= 2;
+    }
+    factorials[0] = 1;
+    inv_factorials[0] = 1;
+    for(int i = 1; i < A; i++) {
+        factorials[i] = factorials[i-1]*i%M;
+        inv_factorials[i] = exp(factorials[i], M - 2);
+    }
+    ll num = 1;
+    for(int i = n-2; i >= 0; i--) {
+        if(modules[i] > modules[i + 1]) {
+            num = num * C(modules[i], modules[i + 1]) % M;
+        }
+        else {
+            num = num * C(modules[i + 1] - 1, modules[i] - 1) % M;
+        }
+    }
+    cout << num;
+}
+