2^x mod n = 1

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/32768 K (Java/Others)

Description

Give a number n, find the minimum x(x>0) that satisfies 2^x mod n = 1.

Input

One positive integer on each line, the value of n.

Output

If the minimum x exists, print a line with 2^x mod n = 1.

Print 2^? mod n = 1 otherwise.

You should replace x and n with specific numbers.

Sample Input

2 5

Sample Output

2^? mod 2 = 1 2^4 mod 5 = 1

Hint

Ignatius.L

Source

ZOJ Monthly, February 2003

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