P401733 - GYM100519 E Equal Digits - SSOJ - 省实信息奥赛评测系统

Memory Limit：256 MB Time Limit：2 S

Judge Style：Text Compare Creator：

Submit：0 Solved：0

上一题 Submit 下一题 Submit Record Statistics MD

E. Equal Digitstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

For the given integer N and digit D, find the minimal integer K ≥ 2 such that the representation of N in the positional numeral system with base K contains the maximum possible consecutive number of digits D at the end.

Input

The input contains two integers N and D (0 ≤ N ≤ 10¹⁵, 0 ≤ D ≤ 9).

Output

Output two integers: K, the answer to the problem, and R, the the number of consecutive digits D at the end of the representation of N in the positional numeral system with base K.

ExamplesInput

3 1

Output

2 2

Input

29 9

Output

10 1

Input

0 4

Output

2 0

Input

90 1

Output

89 2

401733: GYM100519 E Equal Digits

Description

Source/Category

加入题单