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 Specification

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

Output Specification

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.

Sample Input 1

1 9 5

Sample Output 1

1
5

Sample Input 2

1 100 10

Sample Output 2

9
19

Sample Input 3

11111 99999 24

Sample Output 3

5445
11499