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 i in xrange(input()):
	x,m,n=map(int,raw_input().split())
	if x==1:
		print (m+1)%n
	else:
		n*=(x-1)
		tmp=pow(x,m+1,n)
		res=(tmp-1+n)%n
		res/=(x-1)
		print res