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- #include<bits/stdc++.h>
- #define ll long long
- #define Matrix vector< vector < long long > >
- using namespace std;
- Matrix D;
- long long MOD=1000000007;
- void Resize_Matrix(long long n , long long m , Matrix &M){
- M.clear();
- for(int j=0;j<n;j++) {
- M.push_back( vector< long long >() );
- M[j].clear();
- M[j].resize(m);
- for(int i=0;i<m;i++) M[j][i]=0;
- }
- }
- Matrix Matrix_Multiplication(Matrix A , Matrix B){
- Matrix Ans; long long n , m;
- Resize_Matrix(n=A.size() , m=A[0].size() , Ans);
- for(long long j=0;j<n;j++){
- for(long long i=0;i<n;i++){
- Ans[j][i]=0;
- for(long long k=0;k<n;k++){
- Ans[j][i]+=A[j][k]*B[k][i];
- Ans[j][i]%=MOD;
- }
- }
- }
- return Ans;
- }
- Matrix Matrix_Exponentiation(Matrix M , long long power){
- if(power==0)return D;
- if(power==1) return M;
- Matrix ret;
- ret=Matrix_Exponentiation(M , power/2);
- ret=Matrix_Multiplication(ret , ret);
- if(power%2==1) ret=Matrix_Multiplication(ret,M);
- return ret;
- }
- int main()
- {
- int t;cin>>t;
- while(t--)
- {ll k;cin>>k;
- if(k==1){cout<<3<<endl;continue;}
- Matrix F;
- Resize_Matrix(3,3,F);
- Resize_Matrix(3,3,D);
- int q=1;
- for(int i=0;i<3;i++)
- for(int j=0;j<3;j++){
- D[i][j]=1;
- F[j][i]=q;
- q++;
- }
- //for(int i=0;i<3;i++)F[i][i]=1;
- ll sum=0;
- Matrix R;
- Resize_Matrix(3,3,R);
- R=Matrix_Exponentiation(F,k-1);
- for(int i=0;i<3;i++)for(int j=0;j<3;j++)sum=(sum%MOD+R[i][j]%MOD)%MOD;
- cout<<sum<<endl;
- }
- return 0;
- }
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