Cudak

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 $1$.

Sample Input 1 | Sample Output 1 |
---|---|

1 9 5 |
1 5 |

Sample Input 2 | Sample Output 2 |
---|---|

1 100 10 |
9 19 |

Sample Input 3 | Sample Output 3 |
---|---|

11111 99999 24 |
5445 11499 |