int binary_search_last_occurrence(const vector<int>& lst, int target) {    
    if (lst.empty()) return -1;    
    int low = 0, high = lst.size() - 1;    
    while (low < high) {        
        int mid = (low + high + 1) / 2;        
        if (lst[mid] <= target) {            
            low = mid;        
        } else {            
            high = mid - 1;        
        }    
    }    
    if (lst[low] == target)        
        return low;    
    else        
        return -1;
}