Problem B. Before first zero ≡

Statement

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

Consider a sequence B_i 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: B_i = |B_i − 2 − B_i − 1|.

Your program should find such an element B_k that B_k + 1 = 0 and B_j ≠ 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 format

Input file contains two natural numbers N and M.

Output file format

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

Constraints

1 ≤ N, M ≤ 10⁶

Sample tests

1 1

1

2 4

11