|Author:||A. Zhuplev||Time limit:||1 sec|
|Input file:||input.txt||Memory limit:||256 Mb|
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 = |Bi−2 − Bi−1|.
Your program should find such an element Bk that Bk+1 = 0 and Bj ≠ 0 for all 1 ≤ j ≤ k.
In the second sample B1 = 11, B2 = 1111, B3 = 1100, B4 = 11, B5 = 1089, B6 = 1078, …, B151 = 11, B152 = 11, B153 = 0, ….
Input file contains two natural numbers N and M.
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.
1 ≤ N, M ≤ 106
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