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
from collections import defaultdict
N,X,M = map(int,input().split())
ans = 0
d = defaultdict(lambda:-1)
x = X%M
for n in range(M+100):
    if x in d:
        T = n-d[x]
        break
    else:
        d[x] = n
    x *= x
    x %= M
p = 0
y = x
for m in range(d[x],n):
    p += y
    y *= y
    y %= M

ans = 0
n = N
z = X%M
while n:
    ans += z
    n -= 1
    z *= z
    z %= M
    if z==x:
        ans += n//T*p
        n %= T
print(ans)