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=raw_input()
t=int(t)
while t:
	x,m,n=raw_input().split()
	x=int(x)
	m=int(m)
	n=int(n)
	ans=0
	if(x==1):
		ans=(m+1)%n
	else:
		ans=pow(x,m+1,n*(x-1))-1+n*(x-1)
		ans=ans%(n*(x-1))
		ans=ans/(x-1)
	print (ans)
	t=t-1