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Demodogs from the Upside-down have attacked Hawkins again. El wants to reach Mike and also kill as many Demodogs in the way as possible.
Hawkins can be represented as an?n \times nn×n?grid. The number of Demodogs in a cell at the?ii?-th row and the?jj?-th column is?i \cdot ji?j?. El is at position?(1, 1)(1,1)?of the grid, and she has to reach?(n, n)(n,n)?where she can find Mike.
The only directions she can move are the right (from?(i, j)(i,j)?to?(i, j + 1)(i,j+1)?) and the down (from?(i, j)(i,j)?to?(i + 1, j)(i+1,j)?). She can't go out of the grid, as there are doors to the Upside-down at the boundaries.
Calculate the maximum possible number of Demodogs?\mathrm{ans}ans?she can kill on the way, considering that she kills all Demodogs in cells she visits (including starting and finishing cells).
Print?2022 \cdot \mathrm{ans}2022?ans?modulo?10^9 + 7109+7?. Modulo?10^9 + 7109+7?because the result can be too large and multiplied by?20222022?because we are never gonna see it again!
(Note, you firstly multiply by?20222022?and only after that take the remainder.)
輸入格式Each test contains multiple test cases. The first line contains the number of test cases?tt?(?1 \leq t \leq 10^41≤t≤104?). Description of the test cases follows.
The first line of each test case contains one integer?nn?(?2 \leq n \leq 10^92≤n≤109?) — the size of the grid.
輸出格式For each test case, print a single integer — the maximum number of Demodogs that can be killed multiplied by?20222022?, modulo?10^9 + 7109+7?.
題意翻譯給定一個(gè)數(shù)nn,表示有一個(gè)?n \times nn×n?的方格。每個(gè)格子里都有一個(gè)數(shù)，第?ii?行第?jj?列的格子值為?i?ji?j。現(xiàn)在Hawkins要從?(1,1)(1,1)?走到?(n,n)(n,n),每次只能從?(i,j)(i,j)?走到?(i,j+1)(i,j+1)?或?(i+1,j)(i+1,j), 每走到一個(gè)格子就能獲得格子中的一個(gè)數(shù)，大化數(shù)字之和。
輸入格式每個(gè)測(cè)試點(diǎn)包含多個(gè)測(cè)試樣例。第一行包含測(cè)試樣例的數(shù)量?tt, 接下來?tt?行每行一個(gè)數(shù)?nn。表示有?nn?行和?nn?列。
輸出格式共?tt?行，每行一個(gè)數(shù)，表所經(jīng)過的格子乘 2022 后除以?10^9 + 7109+7?的余數(shù)。
輸入輸出樣例輸入 #1復(fù)制
4 2 3 50 1000000000
輸出 #1復(fù)制
14154 44484 171010650 999589541說明/提示
In the first test case, for any path chosen by her the number of Demodogs to be killed would be?77?, so the answer would be?2022 \cdot 7 = 141542022?7=14154?.
題解#importusing namespace std;
#define int long long
int p[4000040];
inline int read()
{
int x=0,f=1;char ch=getchar();
while (ch<'0'||ch>'9'){if (ch=='-') f=-1;ch=getchar();}
while (ch>='0'&&ch<='9'){x=x*10+ch-48;ch=getchar();}
return x*f;
}
int ksm(int a,int b,int mod)
{
int res=1;
while(b)
{
if(b&1)
res=res*a,res%=mod;
a=a*a%mod;
b>>=1;
}
return res;
}
int sum[20000020];
const int mod=1e9+7;
signed main()
{
int T;
cin>>T;
while(T--)
{
int n;
cin>>n;
int ans=n*(n + 1)%mod*(4*n - 1)%mod*ksm(6,mod-2,mod)%mod;
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