# Find the player who wins the game by removing the last of given N cards

Given two integers **N **and **K**, where **N **represents the total number of cards present when game begins and **K** denotes the maximum number of cards that can be removed in a single turn. Two players **A** and **B** get turns to remove at most **K** cards, one by one starting from player A. The player to remove the last card is the winner. The task is to check if **A** can win the game or not. If found to be true, print **‘A’** as the answer. Otherwise, print **‘B’**.

**Examples:**

Input:N = 14, K = 10Output:YesExplanation:

Turn 1: A removes 3 cards in his first turn.

Turn 2: B removes any number of cards from the range [1 – 10]

Finally, A can remove all remaining cards and wins the game, as the number of remaining cards after turn 2 will be ≤ 10

Input:N= 11, K=10Output:No

**Approach:** The idea here is to observe that whenever the value of **N % (K + 1) = 0**, then **A **will never be able to win the game. Otherwise **A **always win the game. **Proof:**

If N ≤ K:The person who has the first turn will win the game, i.e. A.If N = K + 1:A can remove any number of cards in the range[1, K]. So, the total number of cards left after the first turn are also in the range[1, K]. Now B gets the turn and number of cards left are in the range[1, K]. So, B will win the game.If K + 2 ≤ N ≤ 2K + 1:A removes N – (K + 1) cards in his first turn. B can remove any number of cards in the range[1, K]in the next turn. Therefore, the total number of cards left now are in the range[1, K].Now, since the remaining cards left are in the range[1, K], so A can remove all the cards and win the game.

Therefore the idea is to check if** N % (K + 1)** is equal to 0 or not. If found to be true, print B as the winner. Otherwise, print A as the winner.

Below is the implementation of the above approach:

## C++

`// C++ Program to implement` `// the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to check which` `// player can win the game` `void` `checkWinner(` `int` `N, ` `int` `K)` `{` ` ` `if` `(N % (K + 1)) {` ` ` `cout << ` `"A"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"B"` `;` ` ` `}` `}` `// Driver code` `int` `main()` `{` ` ` `int` `N = 50;` ` ` `int` `K = 10;` ` ` `checkWinner(N, K);` `}` |

## Java

`// Java program to implement` `// the above approach` `import` `java.util.*;` `class` `GFG{` `// Function to check which` `// player can win the game` `static` `void` `checkWinner(` `int` `N, ` `int` `K)` `{` ` ` `if` `(N % (K + ` `1` `) > ` `0` `)` ` ` `{` ` ` `System.out.print(` `"A"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `System.out.print(` `"B"` `);` ` ` `}` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `N = ` `50` `;` ` ` `int` `K = ` `10` `;` ` ` ` ` `checkWinner(N, K);` `}` `}` `// This code is contributed by Amit Katiyar` |

## Python3

`# Python3 program to implement` `# the above approach` `# Function to check which` `# player can win the game` `def` `checkWinner(N, K):` ` ` `if` `(N ` `%` `(K ` `+` `1` `)):` ` ` `print` `(` `"A"` `)` ` ` `else` `:` ` ` `print` `(` `"B"` `)` `# Driver Code` `N ` `=` `50` `K ` `=` `10` `# Function call` `checkWinner(N, K)` `# This code is contributed by Shivam Singh` |

## C#

`// C# program to implement` `// the above approach` `using` `System;` `class` `GFG{` `// Function to check which` `// player can win the game` `static` `void` `checkWinner(` `int` `N, ` `int` `K)` `{` ` ` `if` `(N % (K + 1) > 0)` ` ` `{` ` ` `Console.Write(` `"A"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `Console.Write(` `"B"` `);` ` ` `}` `}` `// Driver code` `public` `static` `void` `Main(String[] args)` `{` ` ` `int` `N = 50;` ` ` `int` `K = 10;` ` ` ` ` `checkWinner(N, K);` `}` `}` `// This code is contributed by Amit Katiyar` |

## Javascript

`<script>` ` ` `// Javascript Program to implement` `// the above approach` `// Function to check which` `// player can win the game` `function` `checkWinner(N, K)` `{` ` ` `if` `(N % (K + 1)) {` ` ` `document.write(` `"A"` `);` ` ` `}` ` ` `else` `{` ` ` `document.write(` `"B"` `);` ` ` `}` `}` `// Driver code` ` ` `let N = 50;` ` ` `let K = 10;` ` ` `checkWinner(N, K);` `// This code is contributed by Saurabh Jaiswal` `</script>` |

**Output:**

A

**Time Complexity: **O(1)**Auxiliary Space: **O(1)