J_сетка чисел

#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;


ll S(ll b1, ll q, ll n){
    //return (b1 - b1 * pow(q, n)) / (1 - q);
    ll r = b1 * ( pow(q, n) - 1);
    r %= inf;
    return r;
}

int main()
{
    /*ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);*/
    ll n;
    cin>>n;
    n++;
    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);
        dp[i] = dp[i-1] * ( S(b1, q, i) % inf );
        dp[i] %= inf;
    }
    //cv(dp);
    cout<<dp[n-1];
}