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Prime Game February long challenge 2021 solution with code and explanation

 Prime Game February long challenge 2021 solution with code and explanation  -

Problem statement -

Prime Game February long challenge 2021 solution with code and explanation

Chef and Divyam are playing a game with the following rules:

  • First, an integer X! is written on a board.
  • Chef and Divyam alternate turns; Chef plays first.
  • In each move, the current player should choose a positive integer D which is divisible by up to Y distinct primes and does not exceed the integer currently written on the board. Note that 1 is not a prime.
  • D is then subtracted from the integer on the board, i.e. if the integer written on the board before this move was A, it is erased and replaced by AD.
  • When one player writes 0 on the board, the game ends and this player wins.

Given X and Y, determine the winner of the game.


  • The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
  • The first and only line of each test case contains two space-separated integers X and Y.


For each test case, print a single line containing the string "Chef" if Chef wins the game or "Divyam" if Divyam wins (without quotes).


  • 1T106
  • 1X,Y106


Subtask #1 (5 points): Y=1

Subtask #2 (10 points):

  • 1T102
  • 1X6

Subtask #3 (85 points): original constraints

Example Input

1 2
3 1
2021 42

Example Output



Example case 1: Since D=1 is divisible by 0 primes, Chef will write 0 and win the game in the first move.

Example case 2: Chef must choose D between 1 and 5 inclusive since D=6 is divisible by more than one prime. Then, Divyam can always choose 6D, write 0 on the board and win the game.



Do not try to calculate x! .learn sieve of Eratosthenes this problem is related to this topic.

solution will be posted anytime soon.


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