Processing math: 100%

Problem B. Before first zero

Author:A. Zhuplev   Time limit:1 sec
Input file:input.txt   Memory limit:256 Mb
Output file:output.txt  

Statement

This problem has absolutely no relation to cars and car races.

Consider a sequence Bi defined as follows: First two elements (B1 and B2) are natural numbers whose decimal representations consist of N and M "1" digits correspondingly. Following terms are computed according to the formula: Bi=|Bi2Bi1|.

Your program should find such an element Bk that Bk+1=0 and Bj0 for all 1jk.

In the second sample B1=11, B2=1111, B3=1100, B4=11, B5=1089, B6=1078,, B151=11, B152=11, B153=0,.

Input file format

Input file contains two natural numbers N and M.

Output file format

Output file should contain a single integer — Bk or 0 if there's no zero term in B series. Note that the value of Bk may be very large.

Constraints

1N,M106

Sample tests

No. Input file (input.txt) Output file (output.txt)
1
1 1
1
2
2 4
11

0.076s 0.010s 13