I won't tell you this is about number theory

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

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

Description

To think of a beautiful problem description is so hard for me that let's just drop them off. :)
Given four integers a,m,n,k,and S = gcd(a^m-1,a^n-1)%k,calculate the S.

Input

The first line contain a t,then t cases followed.
Each case contain four integers a,m,n,k(1<=a,m,n,k<=10000).

Output

One line with a integer S.

Sample Input

1 1 1 1 1

Sample Output

0

Hint

yifenfei

Source

ZJFC 2009-3 Programming Contest

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