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())

v = list(range(m))
p = [-1 for _ in range(m)]

a = x
p[a - 1] = 0
s = [x]
l, r = n, n
for i in range(n):
    a = a ** 2 % m
    if p[a - 1] >= 0:
        l, r = p[a - 1], i + 1
        break
    else:
        s.append(a)
        p[a - 1] = i + 1
ans = sum(s[:l])
if l != r:
    b = (n - 1 - i) // (r - l) + 1
    c = (n - 1 - i) % (r - l)
    ans += b * sum(s[l:r]) + sum(s[l:l + c])
print(ans)
