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())
r=[]
s=set()
ans=x
a=x
for i in range(n-1):
    b=a*a%m
    if b in s:
        j = r.index(b)
        N = n-1-i
        T = i-j
        S = sum(r[j:])
        ans += N//T*S
        N %= T
        ans += sum(r[j:j+N])
        break
    else:
        ans+=b
        s.add(b)
        r.append(b)
        a=b
print(ans)