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())

cnt = [x]
c = set()
c.add(x)

for i in range(m+1):
    x = x*x % m
    if x in c:
        break
    cnt.append(x)
    c.add(x)

start = cnt.index(x)

ans = sum(cnt[:start])
roop = len(cnt) - start

n = n-start
ans = ans + (n//roop)*sum(cnt[start:]) + sum(list(cnt)[start:(start+n%roop)])

print(ans)