CERI2018L  Number of divisors of factorial
The goal of the problem is to compute the number of divisors of $\text{Factorial}(n)$.
Input
The first line of the input consist of a single integer number $t$ which determines the number of tests.
In each of next $t$ lines there is two integer numbers $n$ and $m$.
Constraints
 $0 < t < 10^2$ ;
 $0 < n < 2\times10^5$ ;
 $1 < m < 2\times10^9$.
Output
For each test case, print the number of divisors of $n! \pmod m$.
Example
Input: 3 2 1000 3 100 1234 1000000007 Output: 2 4 787315782
Explanation
For the first test case, $2! = 1\times2=2$, whose number of divisors is $2$.
For the second test case, $3! = 1\times2\times3=6$, whose number of divisors is $4$.
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wisfaq:
20180508 14:38:25
whom should be whose

Added by:  Francky 
Date:  20180508 
Time limit:  10s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 