[f(n-2),f(n-1),n^3,n^2,n,1] * A = [f(n-1),f(n),(n+1)^3 ,(n+1)^2,n+1,1]
A = [
0,1,0,0,0,0,
1,1,0,0,0,0,
0,1,1,0,0,0,
0,1,3,1,0,0,
0,1,3,2,1,0,
0,1,1,1,1,1
]
[f(0),f(1),8,4,2,1] * A = [f(1),f(2),27,9,3,1]
[f(0),f(1),8,4,2,1] * A^n = [f(n),f(n=1),f(n+1)^3,f(n+1)^2,n+1,1]
*/ ac_code:
#include<stdio.h>#define ll long longconst ll mod =1e9+7;struct mat
{ll m[10][10];}a,e;
mat operator*(const mat x,const mat y){mat ans;ll tmp;for(int i =0; i <6; i++){for(int j =0; j <6; j++){tmp =0;for(int k =0; k <6; k++){tmp =(tmp%mod+(x.m[i][k]%mod*y.m[k][j]%mod)%mod)%mod;}ans.m[i][j]= tmp;}}return ans;}
mat quickPow(mat a,ll b){mat res = e;while(b){if(b&1)res = res*a;a = a*a;b >>=1;}return res;}intmain(){for(int i =0; i <6; i++){e.m[i][i]=1;a.m[i][1]=1;a.m[5][i]=1;}a.m[5][0]=0;a.m[1][0]=1;a.m[2][2]=1;a.m[3][2]=3;a.m[4][2]=3;a.m[3][3]=1;a.m[4][3]=2;a.m[4][4]=1;ll c[10]={0,1,8,4,2,1};ll t;scanf("%lld",&t);while(t--){ll n;scanf("%lld",&n);mat tp =quickPow(a,n);ll val =0;//f(n)for(int i =0; i <6; i++){val =(val%mod + tp.m[i][0]*c[i]%mod)%mod;}printf("%lld\n",val);}return0;}
