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 = [int(x) for x in input().split()]
s = [0] * (M+10)
s[1] = X
d = {X: 0}
tmp = X
for i in range(M):
    tmp = tmp * tmp % M
    if tmp == 0:
        print(s[i+1])
        exit()
    elif tmp in d:
        l, r = d[tmp], i+1
        sl = s[r] - s[l]
        loop = r-l
        ans = sl*((N-l)//loop) + s[l+(N-l)%loop]
        print(ans)
        exit()
    else:
        d[tmp] = i+1
        s[i+2] = s[i+1] + tmp
print(d)
