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Given the total number of persons **n** and a number **k** which indicates that** k-1 **persons are skipped and **k ^{th}** person is killed in circle in a fixed direction.

The task is to choose the **safe place in the circle** so that when you perform these operations starting from **1**^{st}** ^{ }place** in the circle, you are the last one remaining and survive.

**Example 1:**

**Input:
**n = 3 k = 2
**Output: **3**
Explanation: **There are 3 persons so
skipping 1 person i.e 1st person 2nd
person will be killed. Thus the safe
position is 3.

**Example 2:**

**Input:
**n = 5 k = 3
**Output: **4**
Explanation: **There are 5 persons so
skipping 2 person i.e 3rd person will
be killed. Thus the safe position is 4.

**Your Task:**

You don't need to read input or print anything. You are required to complete the **function josephus ()** that takes** two parameters n and k** and **returns **an integer denoting** safe position**.

**Expected Time Complexity: **O(N).

**Expected Auxiliary Space: **O(N).

**Constraints:**

1 <= k, n <= 20

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Josephus problem

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