Given three integers x, m and n. Evaluate (1 + x + x^ 2 + .. + x^ m)  (mod n)


Input

First line of the input contains a single integer T representing number of test cases that follow.


For next T lines, each line contains three space separated integers x, m and n.


Output

Output exactly T lines each containing the answer to the corresponding test case.


Constraints

1 ≤ T ≤ 1000 
1 ≤ x, n, m ≤ 10^16


Example
Input:
1
3 2 5

Output:
3
t=int(raw_input())
for i in range(0,t):
     x,m,n=map(long,raw_input().split())
     if x==1:
        print (m+1)%n
     else:
         n=n*(x-1)
         ans=pow(x,m+1,n)-1
         ans=(ans+n)%n
         print ans/(x-1)