程序代码：

/*****************************
Input:   (k,N)
       | Ctrl+Z to end
Output:  ans
       | "Error!"
       | "Valid!"
       | "Exit."
*****************************/

#include <iostream>
#include <bitset>

using namespace std;

typedef unsigned long ulong;
typedef unsigned int uint;

ulong An(uint k = 3, uint N = 100);

int main()
{
    uint k = 0, N = 0;
    ulong ans = 0;
   
    while(1){
        cout << "IN: " << flush;
       
        cin.sync();
        cin >> k >> N;
        if(!cin){
            if(cin.eof()){
                cout << "OUT: Exit." << endl;
                return 0;
            }
            else{
                cin.clear();
                cout << "OUT: Error!" << endl;
                continue;   
            }
        }
       
        if(ans = An(k, N)){
            cout << "OUT: " << ans << endl;
        }
        else{
            cout << "OUT: Valid!" << endl;
        }           
    }
   
    return 0;
}

ulong An(uint k, uint N)
{
    if(!((k >= 3 && k <= 15) && (N >= 10 && N <= 1000)))
        return 0;
   
    ulong sum(0), temp(1);   
    bitset<10> coef(N);
   
    for(int i = 0; i < 10; i++){   
            if(coef[i])
                sum += temp;
            temp *= k;
        }
       
    return sum;
}