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 i in range(t):
    a,b,c=raw_input().split()
    a=int(a)
    b=int(b)
    c=int(c)
    if a==1:
    	g=int(((b+1)%c))
    else:
	    g=pow(a,b+1,(a-1)*c)-1+c*(a-1)
	    g%=(a-1)*c
	    g=g/(a-1)
	    g=int(g)
    print g