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=[int(i) for i in raw_input().split()]
x%=m
a=[x]
d={}
d[x]=0
pos=-1
for i in range(1,min(n,100000)):
    t=(a[-1])**2
    t%=m
    if(d.get(t,-1)!=-1):
        pos=d[t]
        break
    d[t]=i
    a.append(t)
s=0
for i in a:
    s+=i
if pos!=-1:
    n-=len(a)
    a=a[pos:]
    s1=0
    for i in a:
        s1+=i
    s+=s1*(n/len(a))
    n%=len(a)
    for i in range(n):
        s+=a[i]
print s
