## Task Description

Write a function `count_day`

to determine the numbers of each day of the week in a particular month.

Given a year, the day of January 1st of that year, and a month, calculate the numbers of Sundays, Mondays, … , Saturdays in that given month. You need to place the results into an array $\textit{results}\lbrack ]$. We use a number from 0 to 6 to represent the day of the week from Sunday to Saturday. For example, 0 means Sunday and 5 means Friday.

Let us illustrate the task with an example. If we are given the year of 2016, February, and the fact that January 1st is a Friday, we need to determine the numbers of each day of the week for February 2016. The answers are that there are 4 Sundays, 5 Mondays, 4 Tuesdays, 4 Wednesdays, 4 Thursdays, 4 Fridays, 4 Saturdays in February 2016. Your program should put the following results in the array $results\lbrack ]$ as follows.

results[0] | results[1] | results[2] | results[3] | results[4] | results[5] | results[6] |
---|---|---|---|---|---|---|

4 | 5 | 4 | 4 | 4 | 4 | 4 |

Note that the given year could be a leap year. A year is a leap year if it is divisible by 400, or it is divisible by 4 but not by 100.

The prototype of `count_day`

is as follows:

1 `void`

`count_day(`

`int`

`year, `

`int`

`day, `

`int`

`month, `

`int`

`results[7]);`

The main program is as follows:

1234567891011121314151617 `#include <stdio.h>`

`#include <stdlib.h>`

`#include "count_day.h"`

`int`

`main(){`

` `

`int`

`year, day, month, results[7] = {0}, i;`

` `

`while`

`(`

`scanf`

`(`

`"%d %d %d"`

`, &year, &day, &month) == 3){`

` `

`for`

`(i = 0; i < 7; i++)`

` `

`results[i] = 0;`

` `

`count_day(year, day, month, results);`

` `

`for`

`(i = 0; i < 6; i++)`

` `

`printf`

`(`

`"%d "`

`, results[i]);`

` `

`printf`

`(`

`"%d\n"`

`, results[i]);`

` `

`}`

` `

`return`

`0;`

`}`

The header file `count_day.h`

is as follows:

1234 `#ifndef COUNTDAY_H_INCLUDED`

`#define COUNTDAY_H_INCLUDED`

`void`

`count_day(`

`int`

`, `

`int`

`, `

`int`

`, `

`int`

`[7]);`

`#endif`

## Input Format

The input contains **multiple test cases.** Each line of input contains three integers $year, day, month$ ($ 0 \lt year \lt 10000$, $0 \leq day \leq 6$, $1 \leq month \leq 12$).

## Output Format

There are **multiple lines** in the output. Each line contains 7 integers that represent the numbers of each day of the week in the particular month.

## Sample Input

12 `2016 5 2`

`2015 4 2`

## Sample Output

12 `4 5 4 4 4 4 4`

`4 4 4 4 4 4 4`

## Compile

`gcc -std=c99 -O2 -c main.c -lm`

`gcc -std=c99 -O2 -c count_day.c -lm`

`gcc -std=c99 -O2 count_day.o main.o -lm`