Easter Sundays

Easter Sunday is a mobile holiday corresponding to the first Sunday after the first full moon of the spring. Write a program to compute the day $D$ and the month $M$ of the Easter Sunday of every given year $Y$ .

Below, := indicates assignment, div indicates integer division, and mod indicates the remainder of the integer division. To solve this problem, use the Gauss method:

Compute
1. $k := Y~\text{div}~100$
2. $x := Y ~\text{mod}~ 19$
3. $b := Y ~\text{mod}~ 4$
4. $c := Y ~\text{mod}~ 7$
5. $q := k~\text{div}~4$
6. $p := (13+8k)~\text{div}~25$
7. $y := (15-p+k-q) ~\text{mod}~ 30$
8. $z := (19x+y) ~\text{mod}~ 30$
9. $n := (4+k-q) ~\text{mod}~ 7$
10. $e := (2b+4c+6z+n) ~\text{mod}~7$
If $z+e \le 9$ , then $D := 22+z+e$ and $M := 3$ .
Otherwise, if $z=29$ and $e=6$ , then $D := 19$ and $M := 4$ .
Otherwise, if $z=28$ and $e=6$ and $x>10$ , then $D := 18$ and $M := 4$ .
Otherwise, $D := z+e-9$ and $M := 4$ .

Input

Input consists of several natural numbers between 1800 and 9999.

Output

Print the day and the month of the Easter Sunday of each year.

Problem information

Author: Unknown
Translator: Carlos Molina

Generation: 2026-01-25T10:26:14.665Z