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())
mn = min(n, m)
P = [] # pre_sum
sum_p = 0 # sum of pre + cycle
X = [-1] * m # for cycle check & pre_len
for i in range(mn):
    if X[x] > -1:
        cyc_len = len(P) - X[x]
        cyc = (sum_p - P[X[x]]) * ((n - X[x]) // cyc_len)
        remain = P[X[x] + (n - X[x]) % cyc_len] 
        print(cyc + remain)
        exit()
    P.append(sum_p)
    sum_p += x
    X[x] = i
    x = x*x % m
print(sum_p)
