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())

ai = x
i = 0

memo = []
d = {}
tmp = 0

while True:
    if ai in d:
        break
    d[ai] = i
    memo.append(ai)

    ai = (ai ** 2) % m
    i += 1

s = d[ai]
e = i
su = sum(memo[s:])

if n <= e+1:
    print(sum(memo[0:n]))
else:
    zan = n - s
    ans = sum(memo[:s]) + (zan // (e-s)) * su
    if zan % (e-s):
        ans += sum(memo[s:s+(zan % (e-s))])
    print(ans)


