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())
if X == 0:
    print(0)
    exit()
tx = X % M
tl = []
ts = set()
ttl = []
for i in range(N):
    tl.append(tx)
    ts.add(tx)
    tx = pow(tx, 2, M)
    if tx in ts:
        ttl = tl[tl.index(tx):]
        break
ans = sum(tl)
if len(ttl)>0:
    d, m = divmod(N-len(tl), len(ttl))
    ans += sum(ttl)*d+sum(ttl[:m])
print(ans)
