Petriukas is conducting a social experiment in his class of n students. He asked every student the same question: "How many friends do you have in this room?"
After collecting all the answers, Petriukas added them together and got a total sum m. However, Petriukas is suspicious. He knows that if student A is friends with student B, then student B is also friends with student A. He also knows that no one can be their own friend.
Help Petriukas determine if the total sum m is possible, or if someone must have made a mistake in their count.
Input
Two integers n and m (1 \le n \le 10^9, 0 \le m \le 2 \cdot 10^{18}), representing the number of students and the total sum of friends reported, respectively.
Output
Print "POSSIBLE" if the sum m is possible, otherwise print "IMPOSSIBLE".
Examples
| standard input | standard output |
|---|
| 3 2
| POSSIBLE
|
| 3 100
| IMPOSSIBLE
|