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 range(input()):
	x,m,n = map(int,raw_input().split());
	if x == 1:
		print (m+1) % n
		continue;
		
	mod = n * (x - 1)
	
	ans = (pow(x,m+1,mod) + mod - 1) % mod
	
	print ans/(x-1)