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=input()
for i in range(0,t):
    x,m,n=list(map(lambda x:int(x),raw_input().split()))
    if(x==1):
        print (m+1)%n
    else:
        n=n*(x-1)
        z=pow(x,m+1,n)
        y=(z-1+n)%n
        print (y/(x-1))