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,raw_input().split())
i=0
v=[x]
t={x:0}
p=0 
start=0
while True: 
    i+=1
    y=(x*x)%m 
    if y in t: 
        p+=(i-t[y]) 
        start+=t[y]
        break 
    t[y]=i
    v.append(y) 
    x=y 
ans=0 

if n<(len(v)): 
    for i in range(n): 
        ans+=v[i] 
    print ans 
else: 
    for i in range(start): 
        ans+=v[i] 
    n-=(start) 
    g=n%p+start
    l=n/p 
    for i in range(start,len(v)): 
        ans+=(l*v[i]) 
        if i<g: 
            ans+=v[i] 
    print ans

    
    
