Algorithms and Data Structures

  • Profound Academy

    • Status
      • 1
        Implementation
      • 2
        Bitwise operations
      • 3
        Prefix Sums
      • 4
        Sliding window / Two pointers
      • 5
        Modular Arithmetic
      • 6
        Number Theory
      • 7
        Binary Search
      • 8
        Basic Sorting
      • 9
        Greedy Algorithms
      • 10
        Basic Dynamic Programming
      • 11
        Recursion
      • 12
        Linked LIst
      • 13
        Queue & Stack
      • 14
        Binary tree + BST
      • 15
        Divide & Conquer + Advanced Sorting
      • 16
        Heap
      • 17
        Hashing
      • 18
        Graph Representation
      • 19
        BFS

  • 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: 1 seconds

    Memory limit: 512 MB

    Output limit: 1 MB

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