Ball Game |2|
~~~~~~~~~~~~~

A group of :math:`N` children decides to play a ball game. Here are the
rules:

-  Each child gets a number from :math:`1` to :math:`N` and these
   numbers are put in a list randomly.

-  The first child in the list has the ball at the beginning of the
   game.

-  Let’s say that this child got the ball with number :math:`k`. Then
   he/she must throw the ball to the child who is in :math:`k^{th}`
   place in the list.

-  For a given number of turns, the game continues like this.

As the children don’t know about programming, they don’t have a clue
about zero-based indexing applied in Python (like in almost every
programming language). In other words, they don’t know that the indices
of the elements in a Python list varies between :math:`0` and
:math:`(N-1)` instead of between :math:`1` and :math:`N`.

Write a function named *ball_game* which takes two arguments. The first
argument is the shuffled list of children’s numbers as a *list of
integers*, where the second one is the number of turns as an *integer*.
This function must return an *integer* as the number of child who has
the ball when the game is over.

Note that if the ball is thrown to the child with number :math:`N`, the
function should terminate the game early without giving any error.

.. container:: sampleio

   Sample I/O:

.. |2| image:: ../../figures/difficulty_four.png
   :class: difficulty

.. code:: default

   >>> ball_game([1, 3, 2], 1)
   1

   >>> ball_game([1, 3, 2], 2)
   3

   >>> ball_game([1, 3, 2], 3)
   3

   >>> ball_game([3, 4, 5, 1, 2], 4)
   2

   >>> ball_game([3, 4, 5, 1, 2], 5)
   5

   >>> ball_game([3, 4, 5, 1, 2], 6)
   5

   >>> ball_game([8, 7, 1, 5, 3, 10, 4, 2, 6, 9], 4)
   3

   >>> ball_game([8, 7, 1, 5, 3, 10, 4, 2, 6, 9], 5)
   5

   >>> ball_game([8, 7, 1, 5, 3, 10, 4, 2, 6, 9], 6)
   10

   >>> ball_game([8, 7, 1, 5, 3, 10, 4, 2, 6, 9], 7)
   10

.. raw:: html

   <button type="button" class="collapsible" onclick="toggle()">

Show the Answer

.. raw:: html

   </button>

.. raw:: html

   <div class="hiddenanswer">

.. code:: python

   def ball_game(list_of_children, number_of_turns):
       t = 0
       i = 0
       while t < number_of_turns:
           try:
               i = list_of_children[i]
           except IndexError:
               break
           t += 1
       return i

.. raw:: html

   </div>