Given two integers N (N <= 10¹⁸) and a prime number P (1 < P < 10¹⁸), find the lowest number x such that there are not N integers greater or equal to 0 whose sum of squares is equal to x.

N = 2, P = 2
x = 3 mod 2 = 1
0 = 02 + 02
1 = 12 + 02
2 = 12 + 12
4 = 22 + 02

Input

The two integers N (1 <= N <= 10¹⁸) and a prime number P (1 < P < 10¹⁸). You have to print the answer modulo P.

Output

You have to print an integer x mod P (-1 < x < 10¹⁸ + 1) that satisfies the problem. If there's no number x, print "Impossible".

Example

Input:
1 3

Output:
2

Input:
13 7

Output:
Impossible