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Little Dima misbehaved during a math lesson a lot and the nasty teacher Mr. Pickles gave him the following problem as a punishment.

Find all integer solutions x (0 < x < 109) of the equation:

x = b·s(x)a + c,

where a, b, c are some predetermined constant values and function s(x) determines the sum of all digits in the decimal representation of number x.

The teacher gives this problem to Dima for each lesson. He changes only the parameters of the equation: a, b, c. Dima got sick of getting bad marks and he asks you to help him solve this challenging problem.

Input

The first line contains three space-separated integers: a, b, c (1 ≤ a ≤ 5; 1 ≤ b ≤ 10000; - 10000 ≤ c ≤ 10000).

Output

Print integer n — the number of the solutions that you've found. Next print n integers in the increasing order — the solutions of the given equation. Print only integer solutions that are larger than zero and strictly less than 109.

        Examples
      
          input
        
3 2 8

          output
        
3
10 2008 13726 

          input
        
1 2 -18

          output
        
0

          input
        
2 2 -1

          output
        
4
1 31 337 967

#include <iostream> 
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <fstream>
#include <algorithm>
#include <climits>
#include <cstring>
#include <string>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <vector>
#include <list>
#define rep(i,m,n) for(i=m;i<=n;i++)
#define rsp(it,s) for(set<int>::iterator it=s.begin();it!=s.end();it++)
const int inf_int = 2e9;
const long long inf_ll = 2e18;
#define inf_add 0x3f3f3f3f
#define mod 1000000007
#define vi vector<int>
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define pi acos(-1.0)
#define pii pair<int,int>
#define Lson L, mid, rt<<1
#define Rson mid+1, R, rt<<1|1
const int maxn=5e2+10;
using namespace std;
typedef  long long ll;
typedef  unsigned long long  ull; 
inline int read(){int ra,fh;char rx;rx=getchar(),ra=0,fh=1;
while((rx<'0'||rx>'9')&&rx!='-')rx=getchar();if(rx=='-')
fh=-1,rx=getchar();while(rx>='0'&&rx<='9')ra*=10,ra+=rx-48,
rx=getchar();return ra*fh;}
//#pragma comment(linker, "/STACK:102400000,102400000")
ll gcd(ll p,ll q){return q==0?p:gcd(q,p%q);}
ll qpow(ll p,ll q){ll f=1;while(q){if(q&1)f=f*p;p=p*p;q>>=1;}return f;}
int dir[4][2] = {{1,0},{-1,0},{0,1},{0,-1}};


ll getsum(ll x)
{
	ll sum1 =0;
	while(x!=0)
	{
		sum1 += x%10;
		x/=10;	
	}
	return sum1;
}




ll a,b,c;
vector<ll> ans;

int main()
{
	ll x;
	//ll re = 0;
	cin >> a>>b>>c;
	for(ll i=1;i<=81;i++)
	{
		ll t =1;
		for(int j=0;j<a;j++)
		{
			t*=i;
		}
		x  = b*t+c;
//		cout << x<<endl;
		if(x>=1e9)
		{
			continue;
		} 
		if(getsum(x)-i==0)
		{

			ans.push_back(x);
		}
	}
	cout << ans.size()<<endl;
	for(int i=0;i<ans.size();i++)
	{
		cout <<" "<< ans[i]; 
	} 
	cout <<endl;
	return 0;
}