#include #define int long long #define endl '\n' #define all(x) x.begin(), x.end() #define sz(x) (int)((x).size()) using namespace std; constexpr int mod = 1e9+7; int fac[400010]; int inv[400010]; int binpow(int a,int b){ if(b==0)return 1; if(b%2){ return (a*binpow(a, b-1))%mod; } else{ return binpow((a*a)%mod, b/2); } } int C(int n,int k){ if(k==0 || k==n)return 1; if(k>n)return 0; return (((fac[n]*inv[k])%mod)*inv[n-k])%mod; } void solve([[maybe_unused]] int test_case){ int n; cin>>n; fac[0]=1; for(int i=1;i<=4*n;i++){ fac[i] = (fac[i-1] * i)%mod; } inv[4*n] = binpow(fac[4*n], mod-2); for(int i=4*n-1;i>0;i--){ inv[i] = (inv[i+1]*(i+1))%mod; } int res=0; int mu[n+1]={0}; for(int i=0;i<=n;i++)mu[i]=1; int pr[n+1]={0}; for(int i=2;i<=n;i++){ if(pr[i]!=0)continue; for(int k = 1; k*i<=n;k++){ pr[i*k] = 1; mu[i*k]*=-1; } for(int k=1;k*i*i<=n;k++){ mu[k*i*i]=0; } } for(int k=1;k<=n;k++){ int a=C(n*4-4*k, n*2); int b = C(n, k); // cout<>test; for(int _=1;_<=test;_++){ solve(_); } return 0; } // C(n*4, n*2) - 4^n * C(n*3, n) // C(n*4 - 4*k, n*2 - 4*k)*C(n, k)