title: Game puzzle, two players playing the game of replacing coin values
body: <p>We have given, n coins with each having some face value k. </p>
  
  <p>Now, there are two players, nick and james playing the game with alternating turn. In each turn, a player can choose any coin and replace it with more than one coins having sum of face value equal to replaced coin. Each of the new coins must be having same equal face value. Integer p is also given, which is the limit denotes that a player can't use the coin for replacement having face value less than p. 
  All players have given unlimited number of coins with unlimited face values.</p>
  
  <p>So sample input will be n,k,p and where n is no. of coin with each face value is k and limit  p is described above. If both play optimally, and nick starts first who will win the game. A player loose the game if he can't able to play its turn (means can't able to replace any of the coin).</p>
  
  <p>Is it game of nim problem or DP? How can we solve this?</p>