Let us denote by f(x, m) the remainder of the Euclidean division of x by m.

Let A be the sequence that is defined by the initial value A_1=X and the recurrence relation A_{n+1} = f(A_n^2, M). Find \displaystyle{\sum_{i=1}^N A_i}.

Constraints

* 1 \leq N \leq 10^{10}
* 0 \leq X < M \leq 10^5
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N X M


Output

Print \displaystyle{\sum_{i=1}^N A_i}.

Examples

Input

6 2 1001


Output

1369


Input

1000 2 16


Output

6


Input

10000000000 10 99959


Output

492443256176507
N,X,M=map(int, input().split())
m=[0]*M
t={}

def f(x,y):
    return x*x % y
a = X
s=0
for i in range(N):
    if a in t:
        x = t[a]
        nn = N - x
        q,r = divmod(nn,i-x)
        s = m[x-1] + (m[i-1] - m[x-1])*q + m[x-1+r] - m[x-1]
        break
    t[a]=i
    s += a
    m[i] = s
    a = f(a,M)
print(s)