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: Wrong Answer)

#include <iostream>
#include <vector>

using namespace std;
typedef long long ll;

constexpr ll MOD = 1e9 + 7;

int main() {
    ll n;
    cin >> n;

    vector<ll> dp(n + 1);
    dp[n] = n;
    ll sum = dp[n];
    for (int i = n - 1; i > 0; i--) {
        //next is 1
        dp[i] = sum;
        if (i + 2 <= n)dp[i] -= dp[i + 2];
        dp[i] += min((int) n - 1, i + 1), dp[i] %= MOD;
        //next is not 1
        dp[i] += (n - 1) * (n - 1), dp[i] %= MOD;
        sum += dp[i], sum %= MOD;
    }

    cout << dp[1] << endl;
    return 0;
}