synchronize 3 threads to print sequential output

I was asked this question in an interview. I was pretty clueless. So I decided to learn some multithreading and hopefully find an answer to this question.

I need to use 3 threads to print the output: 01020304050607.....

1. Thread1: prints 0
2. Thread2: prints odd numbers
3. Thread3: prints even numbers

#include <iostream>
#include <thread>
#include <mutex>
#include <condition_variable>

std::mutex m;
std::condition_variable cv1, cv2, cv3;

int count = 0;

void printzero(int end)
{
    while (count <= end)
    {
        std::unique_lock<std::mutex> lock(m);
        cv1.wait(lock);
        std::cout << 0 << " ";
        ++count;
        if (count % 2 == 1)
        {
            lock.unlock();
            cv2.notify_one();
        }
        else
        {
            lock.unlock();
            cv3.notify_one();
        }
    }
}

void printodd(int end)
{
    while (count <= end)
    {
        std::unique_lock<std::mutex> lock(m);
        cv2.wait(lock);
        if (count % 2 == 1)
        {
            std::cout << count << " ";
            ++count;
            lock.unlock();
            cv1.notify_one();
        }
    }
}

void printeven(int end)
{
    while (count <= end)
    {
        std::unique_lock<std::mutex> lock(m);
        cv3.wait(lock);
        if (count % 2 == 0)
        {
            std::cout << count << " ";
            ++count;
            lock.unlock();
            cv1.notify_one();
        }
    }
}

int main()
{
    int end = 10;

    std::thread t3(printzero, end);
    std::thread t1(printodd, end);
    std::thread t2(printeven, end);

    cv1.notify_one();

    t1.join();
    t2.join();
    t3.join();

    return 0;
}

My solution seems to be in a deadlock situation. I'm not even sure if the logic is correct. Please help