Problem:
Score : 1000 points

Problem Statement

How many infinite sequences a_1, a_2, ... consisting of {{1, ... ,n}} satisfy the following conditions?

The n-th and subsequent elements are all equal. That is, if n \leq i,j, a_i = a_j.

For every integer i, the a_i elements immediately following the i-th element are all equal. That is, if i < j < k\leq i+a_i, a_j = a_k.

Find the count modulo 10^9+7.

Constraints

1 \leq n \leq 10^6

Input

Input is given from Standard Input in the following format:

n

Output

Print how many sequences satisfy the conditions, modulo 10^9+7.

Sample Input 1

2

Sample Output 1

4

The four sequences that satisfy the conditions are:

1, 1, 1, ...

1, 2, 2, ...

2, 1, 1, ...

2, 2, 2, ...

Sample Input 2

654321

Sample Output 2

968545283

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define N 1000005
using namespace std;
const int mod=1e9+7;
int dp[N];
long long S;
int main(){
	int n;cin>>n;
	dp[1]=n;dp[2]=n*1LL*n%mod;
	S=dp[1]+dp[2];
	for(int i=3;i<=n;i++)
		dp[i]=((n-1)*1LL*n-(i-1-2)+S-dp[i-2])%mod,S+=dp[i];
	cout<<dp[n]<<endl;
	return 0;
}