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 = [-1]*10**5; a[x%m] == 0; b = [x%m]
for i in range(1, n):
    x = x**2%m
    if a[x%m] == -1:
        a[x%m] = i; b.append(b[-1]+x%m)
    else:
        s = a[x%m]-1; g = i-1
        print((b[g]-b[s])*((n-s-1)//(g-s))+b[s+(n-s-1)%(g-s)])
        break
else: print(b[-1])