C Program for Calendar

[Karyumi]

Hello, I'm new to C and I need to make a program wherein the user inputs a number (1-12 corresponding to each month) and a year ( from 1978-3000).
The output should be the calendar for the specified date and year.
There should be 7 columns, one for each day. I should also take leap years into consideration which happens every 4 years, but not every 100 years, but happens again every 400 years.

I have this so far.

#include <stdio.h>
#include <string.h>

char month_name[12][9] = {"January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"};

int  day_count(int month, int year)
{
    int day = 0;

    if (month == 1 || month == 3 || month == 5 || month == 7 || month == 8 || month == 10 || month == 12){
        day = 31;
    } else if (month == 4 || month == 6 || month  == 9 || month == 11){
        day = 30;
    } else if (month == 2){
        if (year%4 == 0 && year%100 != 0 && year%400 == 0){
            day = 29;
        } else {
            day = 28;
        }
    }
    
    return day;
}

int first_day(int year)
{
    int init_pos;
    int x;
    int y;
    int z;

    x = (year - 1)/4.0;
    y = (year - 1)/100.0;
    z = (year - 1)/400.0;

    init_pos = (year + x - y + z) % 7;

    return init_pos;
}

int main(void)
{
    int month;
    int year;

    int i;

    do{
        printf("Enter month (1 - 12):     ");
        scanf("%d", &month);
    } while (month < 1 || month > 12);

    do{
        printf("Enter year (1978 - 3000):     ");
        scanf("%d", &year);
    } while (year < 1978 || year > 3000);

    //printf("%s", month_name[month-1]);

    printf("\n       %d Calendar       \n", year);
    printf("%s\n", month_name[month-1]);
    printf("Sun Mon Tue Wed Thu Fri Sat\n");
    
    return 0;
}

I can't think of how I could print out the numbers under the name of the days.
I'm also not sure if my formula for my first_day function will give the right day for each month of the year.

I really need help.
Thanks!

[Subsonics]

You could try something like:

const char *weekday[] = {"Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"};

int i = daynumber % 7;
printf("%s\n", weekday[i]);