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())
L = []
used = set()
while x not in used:
    used.add(x)
    L.append(x)
    x = x*x%m
cnt = 0
while L[cnt] != x:
    cnt += 1
l = len(L)
if n <= l:
    print(sum(L[:n]))
    exit()
s = sum(L)
t = sum(L[cnt:])
q, r = divmod(n-l, l-cnt)
ans = s + q*t
for i in range(r):
    ans += L[cnt]
    cnt += 1
print(ans)