A and B are playing a game. At the beginning there are** n** coins. Given two more numbers x and y. In each move a player can pick x or y or l coins. A always starts the game. The player who picks the last coin wins the game. For a given value of n, find whether A will win the game or not if both are playing optimally.

Examples:

Input : n = 5, x = 3, y = 4 Output : A There are 5 coins, every player can pick 1 or 3 or 4 coins on his/her turn. A can win by picking 3 coins in first chance. Now 2 coins will be left so B will pick one coin and now A can win by picking the last coin. Input : 2 3 4 Output : B

Let us take few example values of n for x = 3, y = 4.

n = 0 A can not pick any coin so he losses

n = 1 A can pick 1 coin and win the game

n = 2 A can pick only 1 coin. Now B will pick 1 coin and win the game

n = 3 4 A will win the game by picking 3 or 4 coins

n = 5, 6 A will choose 3 or 4 coins. Now B will have to choose from 2 coins so A will win.

We can observe that A wins game for n coins only when it loses for coins n-1, n-x and n-y.

## C++

// CPP program to find winner of game // if player can pick 1, x, y coins #include <bits/stdc++.h> using namespace std; // To find winner of game bool findWinner(int x, int y, int n) { // To store results int dp[n + 1]; // Initial values dp[0] = false; dp[1] = true; // Computing other values. for (int i = 2; i <= n; i++) { // If A losses any of i-1 or i-x // or i-y game then he will // definitely win game i if (i - 1 >= 0 and !dp[i - 1]) dp[i] = true; else if (i - x >= 0 and !dp[i - x]) dp[i] = true; else if (i - y >= 0 and !dp[i - y]) dp[i] = true; // Else A loses game. else dp[i] = false; } // If dp[n] is true then A will // game otherwise he losses return dp[n]; } // Driver program to test findWinner(); int main() { int x = 3, y = 4, n = 5; if (findWinner(x, y, n)) cout << 'A'; else cout << 'B'; return 0; }

## Java

// Java program to find winner of game // if player can pick 1, x, y coins import java.util.Arrays; public class GFG { // To find winner of game static boolean findWinner(int x, int y, int n) { // To store results boolean[] dp = new boolean[n + 1]; Arrays.fill(dp, false); // Initial values dp[0] = false; dp[1] = true; // Computing other values. for (int i = 2; i <= n; i++) { // If A losses any of i-1 or i-x // or i-y game then he will // definitely win game i if (i - 1 >= 0 && dp[i - 1] == false) dp[i] = true; else if (i - x >= 0 && dp[i - x] == false) dp[i] = true; else if (i - y >= 0 && dp[i - y] == false) dp[i] = true; // Else A loses game. else dp[i] = false; } // If dp[n] is true then A will // game otherwise he losses return dp[n]; } // Driver program to test findWinner(); public static void main(String args[]) { int x = 3, y = 4, n = 5; if (findWinner(x, y, n) == true) System.out.println('A'); else System.out.println('B'); } } // This code is contributed by Sumit Ghosh

Output:

A

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