Given two integers N ( N <= 10^18 ) and a prime number P ( 1 < P < 10^18 ), find the lowest number x such that there're not N integers greater or equal to 0 whose sum of squares is equal to x.

Input

There're two integers N ( 1 <= N <= 10^18 ) and a prime number P ( 1 < P < 10^18 ). You have to print the answer modulo P.

Output

You have to print an integer x mod P ( -1 < x < 10^18 + 1 ) that satisfies the problem. If there's no number x, print "Impossible".

Example

Input:
1 3
Output:
2
Input:
13 7
Output:
Impossible