1 #include <algorithm>  2 #include <iostream>  3 #include <iomanip>  4 #include <cstring>  5 #include <climits>  6 #include <complex>  7 #include <cassert>  8 #include <cstdio>  9 #include <bitset> 10 #include <vector> 11 #include <deque> 12 #include <queue> 13 #include <stack> 14 #include <ctime> 15 #include <set> 16 #include <map> 17 #include <cmath> 18 using namespace std; 19 #define fr first 20 #define sc second 21 #define cl clear 22 #define BUG puts("here!!!") 23 #define W(a) while(a--) 24 #define pb(a) push_back(a) 25 #define Rint(a) scanf("%d", &a) 26 #define Rll(a) scanf("%I64d", &a) 27 #define Rs(a) scanf("%s", a) 28 #define Cin(a) cin >> a 29 #define FRead() freopen("in", "r", stdin) 30 #define FWrite() freopen("out", "w", stdout) 31 #define Rep(i, len) for(int i = 0; i < (len); i++) 32 #define For(i, a, len) for(int i = (a); i < (len); i++) 33 #define Cls(a) memset((a), 0, sizeof(a)) 34 #define Clr(a, x) memset((a), (x), sizeof(a)) 35 #define Full(a) memset((a), 0x7f7f7f, sizeof(a)) 36 #define lrt rt << 1 37 #define rrt rt << 1 | 1 38 #define pi 3.14159265359 39 #define RT return 40 #define lowbit(x) x & (-x) 41 #define onecnt(x) __builtin_popcount(x) 42 typedef long long LL; 43 typedef long double LD; 44 typedef unsigned long long ULL; 45 typedef pair<int, int> pii; 46 typedef pair<string, int> psi; 47 typedef pair<LL, LL> pll; 48 typedef map<string, int> msi; 49 typedef vector<int> vi; 50 typedef vector<LL> vl; 51 typedef vector<vl> vvl; 52 typedef vector<bool> vb; 53  54 const LL mod =(LL) 1e9+7; 55 const int maxn = 2100001; 56 LL f[maxn]; 57 int n; 58  59 LL mul(LL x, LL n) { 60   LL ret = 1; 61   while(n) { 62     if(n & 1) ret = (ret * x) % mod; 63     n >>= 1; 64     x = (x * x) % mod; 65   } 66   return ret; 67 } 68  69 LL exgcd(LL a, LL b, LL &x, LL &y) { 70   if(b == 0) { 71     x = 1; 72     y = 0; 73     return a; 74   } 75   else { 76     LL ret = exgcd(b, a%b, x, y); 77     LL tmp = x; 78     x = y; 79     y = tmp - a / b * y; 80     return ret; 81   } 82 } 83 LL inv(LL a) { 84   LL x, y; 85   exgcd(a, mod, x, y); 86   return (x % mod + mod) % mod; 87 } 88  89 LL C(LL x, LL y) { 90   return f[x] * inv(f[x-y]) % mod * inv(f[y]) % mod; 91 } 92  93 LL Catalan(int n) { 94   return C(2*n, n) * inv(n+1) % mod; 95 } 96  97 signed main() { 98   // FRead(); 99   f[0] = 1; f[1] = 1;100   For(i, 1, 2000001) f[i] = (f[i-1] * i) % mod;101   int T, _ = 1;102   Rint(T);103   W(T) {104     Rint(n);105     printf("Case #%d:\n%I64d\n", _++, Catalan(n));106   }107   RT 0;108 }