Contents
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.
Input
- 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.
Output
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.
Constraints
- 1≤T≤1061≤T≤106
- 1≤A<B≤10181≤A<B≤1018
- gcd(A,B)=1gcd(A,B)=1
Subtasks
Subtask #1 (100 points): Original constraints
Sample Input
2
1 2
2 3
Sample Output
Yes
No
Explanation
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.
Program:
import io, os, time,sys
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
tests=int(input())
for _ in range(tests):
a,b=map(int,input().split())
if b&(b-1)==0:
sys.stdout.write("Yes\n")
else:
sys.stdout.write("No\n")
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