The number of students

Time limit2sMemory limit256 MB

Summary

Find the smallest numbers of girls and boys whose within-group and cross-group friend counts match the given a, b, c, and d.

Level: Medium5 of 10
Topics: Math, Number theory, Combinatorics
Solved: No attempts yet

Problem

Seonyeong's class has girls and boys. Some pairs of students are friends and some are not. Friendship always goes both ways, so if A is a friend of B, then B is a friend of A. Nobody is their own friend, and a pair of students is friends at most once.

Every girl has exactly $a$ girl friends and exactly $b$ boy friends.

Every boy has exactly $c$ girl friends and exactly $d$ boy friends.

Among the classes that fit these counts, find the one with the fewest students and report how many girls and how many boys it has.

Input

The first line contains $a$ , $b$ , $c$ , $d$ separated by spaces. ( $1 \le a, b, c, d \le 50$ )

Output

Print the number of girls $m$ and the number of boys $n$ on one line, separated by a space. If several classes fit, print the one with the smallest $m$ , which also makes $n$ smallest. Such a class always exists.

Hint

Count the friendships between a girl and a boy from both sides. The girls account for $m \times b$ of them and the boys account for $n \times c$ of them. Those two counts are equal, which fixes the ratio between $m$ and $n$ before anything else.

Examples2

Example 1
Input
```
1 2 1 2
```
Expected output
```
2 4
```
Example 2
Input
```
1 1 1 1
```
Expected output
```
2 2
```