R. Rock Paper Scissors
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

This problem is supposed to be the third easiest one in KUPC2025. It was removed when the contest was ported to Universal Cup.

$$$N$$$ people play one round of rock-paper-scissors.

Determine whether there exists a way for them to choose their hands such that the total number of extended fingers among all players is exactly $$$M$$$.

Furthermore, determine whether, among such ways, there exists at least one in which the game has a winner (that is, it is not a draw).

Input

The first line contains integers $$$N, M$$$ in this order. $$$(2 \leq N \leq 10^{18}, 0 \leq M \leq 10^{18})$$$

Output

If there is no way for all players to choose their hands so that the total number of extended fingers is exactly $$$M$$$, print Impossible.

If such a way exists, then print Yes if there is at least one such way in which the game has a winner (that is, it is not a draw), and print No if there is no such way (that is, no matter how the hands are chosen, the game is always a draw).

Examples
Input
2 7
Output
Yes
Input
3 0
Output
No
Input
4 3
Output
Impossible
Input
123456789123456789 987654321987654321
Output
Impossible
Note

For the first example, if the two players choose scissors and paper, respectively, then the total number of fingers is $$$7$$$, and the game has a winner. Therefore, print Yes.

For the second example, if the three players all choose rock, then the total number of extended fingers is $$$0$$$, but the game is a draw. Since there is no way for the three players to choose hands so that the total number of extended fingers is $$$0$$$ and the game has a winner, print No.

For the third example, there is no way for four players to choose hands so that the total number of extended fingers is $$$3$$$, so print Impossible.

Supplement: rules of rock-paper-scissors

Each person chooses exactly one of the three hands: "rock", "scissors", or "paper". The number of extended fingers for each hand is as follows.

  • Rock: $$$0$$$
  • Scissors: $$$2$$$
  • Paper: $$$5$$$

The rules determining the winner are as follows.

  • Rock beats scissors and loses to paper.
  • Paper beats rock and loses to scissors.
  • Scissors beat paper and lose to rock.

When there are $$$2$$$ players, in addition to the above, the game is a draw if both players choose the same hand. When there are $$$3$$$ or more players, the game has a winner if the hands chosen by all players consist of exactly $$$2$$$ of the $$$3$$$ possible hand types. For example, if among $$$5$$$ players, $$$2$$$ choose paper and $$$3$$$ choose rock, then the $$$2$$$ players who chose paper are the winners. If all players choose the same hand, or if all three hand types appear, then the game is a draw.

(Quoted and partially modified from Wikipedia "Rock paper scissors".)