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())
a = (X*X)%M
lis = [X]
while a not in lis:
    lis.append(a)
    a = a*a%M
i = lis.index(a)
lis1 = lis[:i]
lis2 = lis[i:]
ans=0
if N<=len(lis1):
    ans = sum(lis1[:N])
else:
    ans = sum(lis1)
    n = N - len(lis1)
    ans += (n//len(lis2))*sum(lis2)
    ans += sum(lis2[:n%len(lis2)])
#print(lis1)
#print(lis2)
print(ans)
