7111번 - The Strange Sequence 다국어

문제

There is a sequence of positive integers {a_i}. For each i (i>1) a_i is the least possible integer with the following features:

1. a_i > a_i-1,
2. the sum of a_i digits equals the sum of 4 * a_i-1 digits.

For the given values of the first sequence member a₁ and the index n, you must find and output the value of the a_n.

입력

The values of integers a₁ (0 < a₁ < 20) and n (0 < n < 10000) are input from the keyboard.

출력

You must write one integer on the screen - the value of the a_n. For the testing, only data where the corresponding a_n value does not increase 10⁹ are to be used.

제한

힌트