СПБГУ_J_100_баллов

#include <iostream>
#include <cmath>
#include <vector>
#include <queue>
#include <algorithm>
#include <string>
#include <stack>
#include <set>
#include <map>
#define pii pair <int,int>
using namespace std;
using ll = long long;
using ld = long double;
void cv(vector <ll> &v){
    for (auto x: v) cout<<x<<' ';
    cout<<"\n";
}

ll inf = 1e9 + 7;
vector <ll> lvl; //стпеень 2-ки

ll S(ll b1, ll q, ll n){
    //return (b1 - b1 * pow(q, n)) / (1 - q);
    //ll bin = (pow(q, n) - 1);
    ll bin = lvl[n] - 1;//уже с остатком
    bin %= inf;
    ll r = (b1 % inf) * bin;
    r %= inf;
    return r;
}

int main()
{
    /*ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);*/
    ll n;
    cin>>n;
    n++;
    lvl.resize(n+1);
    lvl[0] = 1;
    for (ll i = 1; i <= n; ++i){
        lvl[i] = lvl[i-1] * 2 % inf;
    }
    //cv(lvl);
    vector <ll> dp(n+1);
    dp[1] = 1;
    ll b1, q=2, num;
    for (ll i = 2; i <= n;++i){
        //b1 = pow(2, n - i);
        b1 = lvl[n-i];
        dp[i] = dp[i-1] * ( S(b1, q, i) % inf );
        dp[i] %= inf;
    }
    //cv(dp);
    cout<<dp[n-1]; //подкорректировать -- сделать так, чтобы
}