Description

You are given a function f: WxW → W, where W represents the set of whole numbers.

The following data is given to you:

• f(4,3)=7
• f(7,8)=15
• f(9,16)=25
• f(10,177)=187
• f(49,76)=125
• f(160,257)=417
• f(165,10)=175
• f(178,213)=103
• f(197,2)=199
• f(199,296)=495
• f(1000,19)=1019
• f(1004,19)=1023

Write a program which calculates f(x, y) given input of two natural numbers.

Input Format

One line containing two space separated integers x and y

Output Format

One line containing the result of f(x, y)

Input Limits

0 < x, y < 1011