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())
loop = []
loop.append(x)
looplist = [0]*m
looplist[x]=1
for i in range(1,m+1):
    x = x**2%m
    #print(x)
    if looplist[x]==0:
        looplist[x]=1
        loop.append(x)
    else:
        break

ss = loop.index(x)
amari = loop[:ss]
neoloop = loop[ss:]

lon = len(neoloop)

if n<=ss:
    print(sum(amari[:n]))
else:
    print(sum(amari)+(n-ss)//lon*sum(neoloop)+sum(neoloop[:(n-ss)%lon]))