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
for _ in range(input()):
    x,m,n=map(int,raw_input().split())
    if x==1: print (m+1)%n;
    else:
        print ((pow(x,m+1,(x-1)*n)-1+(x-1)*n)%((x-1)*n))/(x-1)