GIRLSNBS - Girls and Boys

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There are G girl students and B boy students in a class that is about to graduate. You need to arrange them in a single row for the graduation. To give a better impression of diversity, you want to avoid having too many girls or too many boys seating consecutively. You decided to arrange the students in order to minimize the gender regularity. The gender regularity of an arrangement is the maximum number of students of the same gender (all girls or all boys) that appear consecutively. Given G and B, calculate the minimum gender regularity among all possible arrangements.

Input

Each test case is described using a single line. The line contains two integers G and B representing the number of girls and boys in the class, respectively (0 ≤ G, B ≤ 1000). The end of input is indicated with a line containing the number −1 twice.

Output

For each test case, output a single line with a single integer representing the minimum gender regularity that an arrangement of G girls and B boys can have.

Example

Input: 
10 10
5 1
0 1000
-1 -1
Output:
1
3
1000

hide comments
deerawat: 2020-12-24 18:17:12

YES take care of 0 0

harsh_ag7654: 2020-09-12 17:54:19

take care of 0 0 took me 10 mins to figure out

zimpzamp: 2020-09-01 18:26:20

I was not able to do this by using Pigeon Hole Principle (intentionally) but I rather simulated the whole process because constraints are small.

ckanzz: 2020-08-27 21:26:47

Try using pigeon hole concept, learned something new and really cool, take your time and understand the concept

gauravgupta14: 2020-08-02 05:24:16

hi

amar_shukla1: 2020-06-24 17:23:24

Actually implemented it as I was seeing a pattern.
But then came to know of pigeonhole.Nice concept btw.

pavan_putra: 2020-06-10 13:26:20

pigeon hole :)))))

coolboy7: 2020-06-05 08:59:00

This is one of the easiest questions;)

avi_kumar15: 2020-05-24 11:39:54

use float if u have ceil function *pacefalm*

sahil_19: 2020-04-23 14:17:05

Hint: Use gapping method like in pnc


Added by:Pablo Ariel Heiber
Date:2010-09-27
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 NODEJS OBJC VB.NET
Resource:FCEyN UBA ICPC Selection 2010