lower_bound using recursion

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;

#define ll long long

bool P(ll a, ll key ){
     return a >= key ;
}

int lower_b(ll * a, int last_index  , ll key , int l , int h ){
    if ( l>=h ){
        if ( P(a[l],key)== false ) return last_index+1;
        return l;
    }
    else {
        int mid = l+(h-l)/2;
        if ( P(a[mid],key) ){
            h=mid;
        }
        else {
            l=mid+1;
        }
        return lower_b(a,last_index,key, l, h);
    }
}

int main() {
    int n;
    cin >> n;
    ll * a= new  ll [n];
    for (int i=0;i<n;i++) cin >> a[i];

    ll key;
    cin >> key ;

    cout<<lower_b(a,n-1,key,0,n-1);

    /* Enter your code here. Read input from STDIN. Print output to STDOUT */
    return 0;
}