Marisa loves collecting stuff. In front of her, there are $n$ items, where the $i$-th item has a weight of $w_i$ and a value of $v_i$. She wants to take all of them home, but they are too heavy. Therefore, she decides to only take $k$ items.
If she takes $k$ items, the value of these items is given by:
$$\frac{v_1+v_2+...+v_k}{w_1+w_2+...+w_k}$$
Help Marisa choose items so that the achieved value is maximized.
### Input
- The first line contains two integers $n,k$.
- The next $n$ lines, each line contains two integers $v_i$ and $w_i$.
### Output
- Print a real number, the maximum achievable value. The answer is considered correct if the difference from the correct answer is not greater than $10^{-3}$.
### Constraints
- $1 \le k \le n \le 10^5$.
- $1 \le v_i, w_i \le 10^9$.
### Example
Input:
```
5 3
1 3
2 2
2 5
4 2
1 4
```
Output:
```
1.0000000000
```
