~cpp 
import junit.framework.TestCase;

public class MyTest extends TestCase {
    private HowManyZerosAndDigits object;
    
    public void testFactorial() {
        object = new HowManyZerosAndDigits(0, 0);
        assertEquals(1, object.factorial(1));
        assertEquals(2, object.factorial(2));
        assertEquals(6, object.factorial(3));
        assertEquals(24, object.factorial(4));
    }
    
    public void testHowManyZeros() {
        object = new HowManyZerosAndDigits(0, 0);
        assertEquals(0, object.howManyZeros(1));
        assertEquals(1, object.howManyZeros(10));
        assertEquals(2, object.howManyZeros(100));
        assertEquals(2, object.howManyZeros(1010));
    }
    
    public void testNumberSystemConversion() {
//        object = new HowManyZerosAndDigits(120, 16);
//        assertEquals(2, object.convertNumber());
//        
//        object = new HowManyZerosAndDigits(120, 10);
//        assertEquals(3, object.convertNumber());
    }
}
 

~cpp 
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.LinkedList;


public class HowManyZerosAndDigits {
    private int _n;
    private int _b;
    private int _fact;
    private LinkedList numbers;

    public HowManyZerosAndDigits(int n, int b) {
        _n = n;
        _b = b;
        numbers = new LinkedList();
    }
    
    public void solve() {
        _fact = factorial(_n);
        convertNumber();
        System.out.println(howManyZeros() + " " + numDigit());
    }
    
    public int factorial(int n) {
        int result = 1;
        for(int i=1; i<n+1; ++i) {
            result = result*i;
        }
        return result;
    }
    
    public void convertNumber() {
        if( _b == 10 )
            return;

        int quotient = _fact / _b;
        int remainder = _fact % _b;
        
        if( remainder != 0 )
            numbers.add(new Long(remainder));
        
        while( quotient != 0 ) {
            remainder = quotient % _b;
            quotient = quotient / _b;
            if( !(quotient==0 && remainder==0)) // 제일 상위자리가 0인 경우는 넣지 않는다.  
                numbers.add(new Long(remainder));
        }
    }
    
    public int howManyZeros(long num) {
        int count = 0;
        String number = Long.toString(num);
        
        for(int i=0; i<number.length(); ++i) {
            if( number.charAt(i)== '0' )
                ++count;
        }
        return count;
    }
    
    public int howManyZeros() {
        if( _b == 10 ) {
            return howManyZeros((long)_fact);
        }
        else {
            int count = 0;
	        Object arr[] = numbers.toArray();
	        for(int i=0; i<arr.length; ++i) {
	            Long l = (Long)arr[i];
	            count += howManyZeros(l.longValue());
	        }
	        return count;
        }
    }
    
    public int numDigit() {
        if( _b == 10 ) {
            int count = 1, value = _fact;
            value = value/_b;
            
            while( value != 0 ) {
                value = value/_b;
                ++count;
            }
            return count;
        } else {
            return numbers.size();
        }
    }
    
    public static void main(String args[]) {
        try {
            int n = readInt();
            int b = readInt();
            HowManyZerosAndDigits h = new HowManyZerosAndDigits(n, b);
            h.solve();
            
        } catch(Exception ex) {
            ex.printStackTrace();
        }
    }
    public static int readInt() throws Exception {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        String intVal = reader.readLine();
        return Integer.parseInt(intVal);
    }
}