From Rational to Binary Codechef Solution

From Rational to Binary Solution Problem Code: REALBIN

Chef and Divyam are playing a game. They start with a rational number XX, such that 0<X<10<X<1.

In each turn, Chef chooses a positive real number YY. Then Divyam either adds or subtracts YY to XX. So XX is replaced with either X+YX+Y or X−YX−Y. If this number becomes 00 or 11, then Chef wins. Otherwise, the game continues.

You are given XX, and you have to determine whether Chef can win in a finite number of moves. More formally, does there exist a finite number NN so that Chef has a strategy that is guaranteed to win in at most NN moves?

Here, XX will be given in the form ABAB, where AA and BB are positive integers, A<BA<B and gcd(A,B)=1gcd(A,B)=1.


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


For each test case, print a single line containing the string "Yes" if Chef can win the game in a finite number of moves and "No" otherwise (without quotes). You can print "Yes" or "No" in any case.


  • 1≤T≤1061≤T≤106
  • 1≤A<B≤10181≤A<B≤1018
  • gcd(A,B)=1gcd(A,B)=1


Subtask #1 (100 points): Original constraints

Sample Input

1 2
2 3

Sample Output



Test case 1: Chef will choose Y=12Y=12, so whatever Divyam does, the number will become 00 or 11. Hence Chef will win in a finite number of moves.

Test case 2: No matter what Chef chooses, it can be shown that Divyam can make sure Chef never wins.


import io, os, time,sys

input = io.BytesIO(, os.fstat(0).st_size)).readline
for _ in range(tests):
    if b&(b-1)==0:

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