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.

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

-----Output-----
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 $1$.

-----Examples-----
Sample Input 1:
1 9 5
Sample Output 1:
1
5

Sample Input 2:
1 100 10
Sample Output 2:
9
19

Source: kattis | Difficulty: HARD


Solutions: