Best guess in the random game

Interview

Time limit1sMemory limit256 MB

Summary

Pick the number from 1 to N whose interval of radius K covers the most hidden values and report its coverage count.

Level: Easy2 of 10
Topics: Math, Intervals
Solved: No attempts yet

Problem

The grader picks one integer uniformly at random between 1 and $N$ . Call that integer $R$ . Without seeing $R$ , you print one integer $X$ between 1 and $N$ , and you win when $|X - R| \le K$ .

Find the $X$ that wins with the highest probability. When several values of $X$ tie, take the smallest one. Also count how many values of $R$ let that $X$ win.

Input

The first line contains two integers $N$ and $K$ separated by one space. ( $1 \le N \le 10^9$ , $0 \le K \le 10^9$ )

Output

On the first line, print the smallest $X$ among those with the highest winning probability, then the number of values of $R$ that satisfy $|X - R| \le K$ for that $X$ , separated by one space.

Examples3

Example 1
Input
```
10000 100
```
Expected output
```
101 201
```
Example 2
Input
```
1 0
```
Expected output
```
1 1
```
Example 3
Input
```
5 10
```
Expected output
```
1 5
```