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
#include <bits/stdc++.h>
#define rei register int
#define int long long
using namespace std;
const int maxn = 100010;
int n,m,x;
int f[maxn][40],s[maxn][40];
signed main(){
	cin >> n >> x >> m;
	for(rei i = 0;i <= m - 1;++i)
	f[i][0] = 1ll*i * i % m,s[i][0] = f[i][0];
	for(rei j = 1;j <= 39;++j)
	 for(rei i = 1;i <= m - 1;++i)
	f[i][j] = f[f[i][j - 1]][j - 1],s[i][j] = s[f[i][j - 1]][j - 1] + s[i][j - 1];
	int ans(0),now(x); --n;
	for(rei i = 39;i >= 0;--i) if(((long long)1 << (long long)i) <= n){
		n -= ((long long)1 << (long long)i);
		ans += s[now][i],now = f[now][i];
	} ans += x; cout << ans << endl; return 0;
}