Božo is a strange little boy. Every day he tires his friends with strange questions. Today's question is: how many integers in the interval \([A, B]\) are there such that the sum of their digits is \(S\), and which is the smallest such number?

Write a program that answers Božo's question so that he can get some sleep.

The input contains three integers \(A\), \(B\) and \(S\) (\(1 \le A \le B < 10^{15}\), \(1 \le S \le 135\)).

The first line should contain the number of integers in the interval with the digit sum equal to \(S\).

The second line should contain the smallest such integer.

The input data will guarantee that the first number is at least \(1\).

Scoring: For correctly outputting one of the two numbers you will receive \(50\%\) of the score.

Note: if you want to receive credit for just the second number, be sure to output something (\(0\), for example) as the first number so the judge can interpret your output correctly.

riseoj 작성

출처 COCI 2007/2008 Contest 3