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
def main():
    t=int(input())
    while t>0:
        t=t-1
        x,m,n=map(int,raw_input().split())
        if x==1:
            print (m+1)%n
        else:
            temp=(x-1)*n
            s=pow(x,m+1,temp)
            s=(s-1+(temp))%temp
            s/=(x-1)
            print s
    return 0
main()