In the currently used Gregorian calendar, there are $365$ days and $366$ days for a normal year and a leap year, respectively. The rule for leap years is as follows.
For year $y$ that is exactly divisible by four is a leap year, except for years that are exactly divisible by $100$, but these centurial years are leap years if they are exactly divisible by $400$. For example, the years $1700$, $1800$, and $1900$ are not leap years, but the years $1600$ and $2000$ are.
The days of the week can be represented as weekday numbers: Sunday as $0$, Monday as $1$, Tuesday as $2$ and so on. If we know $y$ and the day $d$ of the January $1$, we can calculate the day of any specific date $x$ by calculating the remainder of $elapsed\_days\_in\_year\_y(x)$ after division by $7$ and shifting $d$ days.
Write a program that reads $y$, $d$ and $x$, and then displays the weekday number of the date $x$.
The first line contains two integers $y$ and $d$, separated by a space.
The second line contains two integers to represent month and day of the date $x$, respectively.
If $x$ is a legal date, display the weekday number of $x$. If the month of $x$ is illegal, display $-1$. If the date of $x$ is illegal, display $-2$.
You can assume there is no testdata that the month and the date are both illegal.
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