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