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())
X = [-1] * m
P = []
sum_p = 0
while X[x] == -1: # preset
    X[x] = len(P) # pre length
    P.append(sum_p) # pre sum_p
    sum_p += x # now sum_p
    x = x*x % m
P.append(sum_p) # full sum_p

p_len = len(P) - 1
if n <= p_len:
    print(P[n]) # sum_p
    exit()

cyc_times, nxt_len = divmod(n - X[x], p_len - X[x])
cyc = (sum_p - P[X[x]]) * cyc_times
remain = P[X[x] + nxt_len]
print(cyc + remain)
