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
#!/usr/local/bin/python3

N, X, M = map(int, input().split())

def f(x, m):
    return x**2 % m

check = [False for _ in range(M)]
d = [X]
max_x = 0
for _ in range(1, N+1):
    X = f(X, M)
    if check[X]:
        break
    else:
        check[X] = True
    d.append(X)

idx = d.index(X)
ans = sum(d[:idx])
N -= idx
d = d[idx:]

sumd = sum(d)
ans += N//len(d) * sumd

ans += sum(d[:N%len(d)])

print(ans)
