ACM ICPC LA (Live Archive) 3619 solution in Java

import java.io.*;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class SumOfDifferentPrimes {

    public static class SieveOfEratosthenes {
        private boolean[] a;

        public SieveOfEratosthenes(int N) {
            a = new boolean[N + 1];
            for (int i = 0; i < N; i++) {
                a[i] = true;
            }
            a[0] = false;
            a[1] = false;

            int root = (int) Math.sqrt(N);
            for (int i = 2; i <= root; i++) {
                for (int j = 2 * i; j <= N; j += i) {
                    a[j] = false;
                }
            }
        }

        public boolean isPrime(int n) {
            return a[n];
        }

        public List<Integer> getPrimes() {
            List<Integer> list = new ArrayList<Integer>();
            for (int i = 1; i < a.length; i++) {
                if (a[i]) {
                    list.add(i);
                }
            }
            return list;
        }
    }

    public static void main(String[] args) throws FileNotFoundException {
        InputReader in = new InputReader(System.in);
        SieveOfEratosthenes soe = new SieveOfEratosthenes(1120);
        List<Integer> primes = soe.getPrimes();
        int[][][] arr = new int[primes.size() + 1][1121][15];

        arr[0][0][0] = 1;

        for (int i = 1; i < primes.size() + 1; i++) {
            int prime = primes.get(i - 1);

            for (int j = 0; j <= 1120; j++) {
                for (int k = 0; k <= 14; k++) {
                    if ((j + prime) <= 1120 && k < 14) {
                        arr[i][j + prime][k + 1] += arr[i - 1][j][k];
                    }
                    arr[i][j][k] += arr[i - 1][j][k];
                }
            }
        }

        while (true) {
            int n = in.nextInt();
            int k = in.nextInt();
            if (n == 0 && k == 0) break;
            if (n == 0 || k == 0) {
                System.out.println(0);
                continue;
            }
            System.out.println(arr[primes.size()][n][k]);
        }
    }

    public static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
    }
}

Sample Input:

24 3
24 2
2 1
1 1
4 2
18 3
17 1
17 3
17 4
100 5
1000 10
1120 14
0 0

Sample Output:

2
3
1
0
0
2
1
0
1
55
200102899
2079324314