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())

li = [x]
a = x
q = 0
flag = False
for i in range(m):
    k = (a**2)%m
    if k == 0:
        p = i+1
        flag = True
        break
    if k in li:
        p = i+1
        q = li.index(k)
        break
    li.append(k)
    a = k
    
K = sum(li)
li2 = li[q:]
K2 = sum(li2)

if not flag:
    ans = K + ((n-p)//(p-q))*K2 + sum(li2[:((n-p)%(p-q))])
else:
    ans = sum(li[:n])
print(ans)