Happy Numbers

Schoolboy Vasya has a fondness for numbers that end with his lucky digit k. Whenever he encounters a natural number n, he eagerly seeks a base d (where d ≥ 2) such that the representation of n in base d ends with the maximum possible sequence of the digit k.

Your task is to develop a program that, given the numbers n and k, determines the base d for which the representation of n in base d ends with the longest sequence of the digit k.

Input Format

The input consists of two decimal integers n and k (1 ≤ n ≤ 10^{11}; 0 ≤ k ≤ 9).

Output Format

Output two numbers: d — the base of the numeral system, and s — the number of consecutive k digits that the representation of n ends with in this base. If there are multiple bases d that achieve this, choose the smallest one.

Examples