The Last Bus Trip

Version: Phuoc Hung OJ Extended

Problem Statement

There are $N$ students to transport using a vehicle with capacity $K$. Every trip before the last carries $K$ students whenever at least $K$ students remain. Determine the minimum number of trips and the number of students on the last trip.

Input

One line contains two positive integers $N$ and $K$.

Output

Print two integers: the minimum number of trips and the number of students on the last trip.

Subtasks

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

Examples

Example 1

Input

23 8

Output

3 7

Explanation

The first two trips carry $16$ students, leaving $7$ for the last trip, for $3$ trips in total.

Example 2

Input

40 10

Output

4 10

Explanation

$40$ is divisible by $10$, so there are $4$ trips and the last trip still carries $10$ students.

Example 3

Input

1 50

Output

1 1

Explanation

There is only one student, so exactly one trip is needed and it carries $1$ student.