AMR10I - Dividing Stones

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There are N stones, which can be divided into some piles arbitrarily. Let the value of each division be equal to the product of the number of stones in all the piles modulo P. How many possible distinct values are possible for a given N and P?
 
INPUT
The first line contains the number of test cases T. T lines follow, one corresponding to each test case, containing 2 integers: N and P.
 
OUTPUT
Output T lines, each line containing the required answer for the corresponding test case.
 
CONSTRAINTS
T <= 20
2 <= N <= 70
2 <= P <= 1e9
 
SAMPLE INPUT
2
3 1000
5 1000
 
SAMPLE OUTPUT
3
6
 
EXPLANATION
In the first test case, the possible ways of division are (1,1,1), (1,2), (2,1) and (3) which have values 1, 2, 2, 3 and hence, there are 3 distinct values.
In the second test case, the numbers 1 to 6 constitute the answer and they can be obtained in the following ways:
1=1*1*1*1*1
2=2*1*1*1
3=3*1*1
4=4*1
5=5
6=2*3



Added by:Varun Jalan
Date:2010-12-13
Time limit:0.981s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:own problem, ICPC Asia regionals, Amritapuri 2010