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()
while t>0:
    t-=1
    l=raw_input()
    z=l.split(" ")
    x = int(z[0])
    m = int(z[1])
    n = int(z[2])
    if x==1:
        print (m+1)%n
    else:
        n = n*(x-1)
        ans = pow(x,m+1,n)-1
        ans=(ans+n)%n
        ans/=x-1
        print ans