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 t in range(T):
	x,m,n=map(int,raw_input().split())
	if x == 1:
		print (m+1)%n
	else:
		n=n*(x-1)
		res = (pow(x, m+1, n)-1)
		res = (res+n)%n
		print int(res/(x-1))