Consider positive integers A and B. Your task is to represent A as the algebraic sum of integer powers of B with the minimal possible number of terms. In other words,

where si = -1 or si = 1, ki are integers and n should be minimized.

Input

The first line contains positive integer A written without leading zeroes. A contains no more than 3000 digits. Second line contains integer B (1 ≤ B ≤ 106).

Output

Print one integer number n.