Description

Let us consider the set of integer numbers between 1 and N inclusive. Let us order them lexicographically (i. e. like in the vocabulary), for example, for N = 11 the order would be: 1, 10, 11, 2, 3, 4, 5, 6, 7, 8, 9.

Let us denote the position of the number K in this ordering as Q_N,K

. For example, Q

_11,2

= 4. Given numbers K and M find the smallest N such that Q

_N,K

= M.

Input

Input contains two integer numbers K and M (1 <= K, M <= 10

⁹

) separated by a space.

Output

If such N that Q

_N,K

= M exists then write to the output the smallest such N, otherwise write 0.

100000001 1000000000

100000000888888879

Source

Northeastern Europe 2002