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())

ans = 0
a = [0]
id = [0]*(m+1)
l = 1
while id[x] == 0:
    a.append(x)
    id[x] = l
    ans += x
    l += 1
    x = x**2 % m

c = l - id[x]
s=0

for i in range(id[x],l):
    s += a[i]

if n <= l-1:
    ans = 0
    for i in range(1,n+1):
        ans += a[i]
else:
    n -= l
    n += 1
    ans += s*(n//c)
    n %= c
    for i in range(n):
        ans += a[id[x] + i]
print(ans)