How to write the particular structures from array to new.txt file and nothing more?

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C++

Hello, guys.

Firstly, my program’s function fillCards saves a name and a surname in the structure and then writes it to cards.txt file. Then the function readCard reads structures to the array and show them. When user enters the number of structure, the function writes the structures of the array (except the structure which number is the same as the user’s entered number) to new.txt file. The problem is that new.txt file is filled with the same number of structures as cards.txt and instead of ignored structures the last structure is repeatedly written. How to write the particular structures from array to new.txt file and nothing more? I will be very greatful for any help.

#include <iostream>
#include <fstream>
#include <string>
#include <cstring>

using namespace std;

struct card {
       char name[40];
       char surname[40];
};

card A = {"Anna", "Karenina"};
card S;

int fillCards() {

    //cards.txt is filled with stuctures
    char answer;
    int i = 0;

    ofstream file ("cards.txt", ios::binary);
    if (!file)
    cerr << "Unable to open cards.txt" << endl;

    do
    {
    i++;
    char word1 [40];
    char word2 [40];

    cout << "Enter a name..." << endl;
    cin >> word1;

    cout << "Enter a surname..." << endl;
    cin >>word2;


    strcpy (A.name, word1);
    strcpy (A.surname, word2);

    file.write((char *) &A, sizeof(card));

    do {
        cout << "Would you like to enter next person? (Y/N)" << endl;
        cin >> answer;
        answer = toupper(answer);
        }
    while ((answer != 'Y') && (answer != 'N'));
    }
    while ( answer == 'Y');

    file.close();

    return 0;
}


int readCards() {

    int i, k, length;


    //Structures are read to array from card.txt file

    ifstream file ("cards.txt", ios::binary);

    if (!file)
    cerr << "Unable to open cards.txt" << endl;

    file.seekg (0, ios::end);
    length = file.tellg();
    file.seekg (0, ios::beg);

    i = length/sizeof(card);

    card *arr = new card[i];

    for (int n = 0; n < i; n++) {
    file.read((char *) &S, sizeof(card));
    arr[n] = S;
    cout << (n+1) << " " << arr[n].name << " " << arr[n].surname << endl;
    }

    file.close();

    //Structures are written to new.txt file
    _unlink("cards.txt");
    
    ofstream rubber ("new.txt", ios::binary);

    if (!rubber)
    cerr << "Unable to open new.txt" << endl;

    cout << "Enter a number of person which you want to delete" << endl;
    cin >> k;

    for (int x = 0; x < i; x++) {
    if ((x + 1) != k ){
                rubber.write((char *) &arr[x], sizeof(card));
                cout << (x + 1) << " " << arr[x].name << " " << arr[x].surname << endl;
                    }
    }

    rubber.close();

    delete[] arr;

    return 0;
}


int showCards () {

    //Read new.txt file and show it to the user

    cout << "\nNaujas turinys" << endl;

    int m = 0;
    ifstream file ("new.txt", ios::binary);

    if (!file)
    cerr << "Unable to open new.txt" << endl;

    while((!file.eof()) && (!file.fail())) {
    m = m + 1;
    file.read((char *) &S, sizeof(card));
    cout << m << " " << S.name << " " << S.surname << endl;
    }

    file.close();
    return 0;
}

int main() {

    fillCards();
    readCards();
    showCards();

    return 0;
}

I've corrected mistake of number of the dynamic array's elements. But still my problem exists.
For example the contents of cards.txt :
1 Charlotte Smith
2 Emma Jones
3 Sophia Baker
4 Bernadette Soubirous

Then I choose number 2 (the value of k) and then program writes elements of array to new.txt except the element with Emma Jones. The contents of new.txt look like this:
1 Charlotte Smith
2 Sophia Baker
3 Bernadette Soubirous
4 Bernadette Soubirous

But I need the contents of new.txt to be like this:
1 Charlotte Smith
2 Sophia Baker
3 Bernadette Soubirous

Any ideas?