1543: CF833 - A. The Meaningless Game
[Creator : ]
Description
Slastyona and her loyal dog Pushok are playing a meaninglessgamethat is indeed very interesting.
Thegameconsists of multiple rounds. Its rules are very simple: in each round, a natural number $k$ is chosen. Then, the one who says (or barks) it faster than the other wins theround. After that, the winner's score is multiplied by $k^2$, and the loser's score is multiplied by $k$. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all $n$ games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Thegameconsists of multiple rounds. Its rules are very simple: in each round, a natural number $k$ is chosen. Then, the one who says (or barks) it faster than the other wins theround. After that, the winner's score is multiplied by $k^2$, and the loser's score is multiplied by $k$. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all $n$ games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games $n\ (1≤n≤350,000)$ is given.
Each game is represented by a pair of scores $a,b\ (1≤a,b≤10^9)$ — the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
Sample 1 Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Sample 1 Output
Yes
Yes
Yes
No
No
Yes
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.