Next Signal Time

Version: Phuoc Hung OJ Extended

Problem Statement

A signal first turns on at time $A$ and then every $K$ time units, at times $A,A+K,A+2K,\ldots$. Given $T\ge A$, find the earliest signal time not smaller than $T$ and the waiting time from $T$ to that signal.

Input

One line contains three positive integers $A$, $K$, and $T$.

Output

Print two integers: the earliest signal time not smaller than $T$ and the corresponding waiting time.

Subtasks

• Subtask 1 (30 points):
  • $1 \le A \le T \le 10^6$.
  • $1 \le K \le 10^6$.
• Subtask 2 (70 points):
  • $1 \le A \le T \le 10^{18}$.
  • $1 \le K \le 10^{18}$.

Examples

Example 1

Input

4 6 17

Output

22 5

Explanation

The signal times around $17$ are $16$ and $22$. The first one not smaller than $17$ is $22$, so the wait is $22-17=5$.

Example 2

Input

10 5 25

Output

25 0

Explanation

$25=10+3\cdot5$ is exactly a signal time, so the earliest signal not smaller than $25$ is $25$ itself and the wait is $0$.

Example 3

Input

1 100 2

Output

101 99

Explanation

After time $1$, the next signal is at $101$. Since $2$ lies between them, the answer is $101$ with a wait of $99$.