Algorithms and Data Structures

Find sqrt(n) with precision

Given a positive integer n, it’s possible to find the with precision using binary search. You are asked to find the square root of n with precision by performing a binary search on the result k times.

Input

The input contains two integers n (2 ≤ n ≤ ) and k (1 ≤ k ≤ 100).

Output

The program should print the with a precision of performing k binary search splits.

Examples

Input
Output
10 2
3.75

Explanation

Iteration 1: (0 + 10) / 2 = 5 ⇒ lower ⇒ (0, 5)
Iteration 2: (0 + 5) / 2 = 2.5 ⇒ higher ⇒ (2.5, 5)
Stop ⇒ (2.5 + 5) / 2 = 3.75
 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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