A thief made his way to a shop.

As usual he has his lucky knapsack with him. The knapsack can contain k objects. There are n kinds of products in the shop and an infinite number of products of each kind. The cost of one product of kind i is ai.

The thief is greedy, so he will take exactly k products (it's possible for some kinds to take several products of that kind).

Find all the possible total costs of products the thief can nick into his knapsack.

Input

The first line contains two integers n and k (1 ≤ n, k ≤ 1000) — the number of kinds of products and the number of products the thief will take.

The second line contains n integers ai (1 ≤ ai ≤ 1000) — the costs of products for kinds from 1 to n.

Output

Print the only line with all the possible total costs of stolen products, separated by a space. The numbers should be printed in the ascending order.

Examples

Input

3 2
1 2 3


Output

2 3 4 5 6


Input

5 5
1 1 1 1 1


Output

5


Input

3 3
3 5 11


Output

9 11 13 15 17 19 21 25 27 33
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Reader;
import java.util.StringTokenizer;

// Educational Codeforces Round 9
// Thief in a Shop
public class Problem_632_E {
    

    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        Problem_632_E solver = new Problem_632_E();
        solver.solve(1, new InputStreamReader(inputStream), out);
        out.close();
    }
    
    static class FastFourierTransform {
      public static void fft(double[] a, double[] b, boolean invert) {
        int count = a.length;
        for (int i = 1, j = 0; i < count; i++) {
          int bit = count >> 1;
        for (; j >= bit; bit >>= 1)
          j -= bit;
        j += bit;
        if (i < j) {
          double temp = a[i];
          a[i] = a[j];
          a[j] = temp;
          temp = b[i];
          b[i] = b[j];
          b[j] = temp;
        }
        }
        for (int len = 2; len <= count; len <<= 1) {
          int halfLen = len >> 1;
        double angle = 2 * Math.PI / len;
        if (invert)
          angle = -angle;
        double wLenA = Math.cos(angle);
        double wLenB = Math.sin(angle);
        for (int i = 0; i < count; i += len) {
          double wA = 1;
          double wB = 0;
          for (int j = 0; j < halfLen; j++) {
            double uA = a[i + j];
            double uB = b[i + j];
            double vA = a[i + j + halfLen] * wA - b[i + j + halfLen] * wB;
            double vB = a[i + j + halfLen] * wB + b[i + j + halfLen] * wA;
            a[i + j] = uA + vA;
            b[i + j] = uB + vB;
            a[i + j + halfLen] = uA - vA;
            b[i + j + halfLen] = uB - vB;
            double nextWA = wA * wLenA - wB * wLenB;
            wB = wA * wLenB + wB * wLenA;
            wA = nextWA;
          }
        }
        }
        if (invert) {
          for (int i = 0; i < count; i++) {
            a[i] /= count;
            b[i] /= count;
          }
        }
      }

      public static boolean[] multiply(boolean[] a, boolean[] b) {
        int resultSize = Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2;
        resultSize = Math.max(resultSize, 1);
        double[] aReal = new double[resultSize];
        double[] aImaginary = new double[resultSize];
        double[] bReal = new double[resultSize];
        double[] bImaginary = new double[resultSize];
        for (int i = 0; i < a.length; i++)
          aReal[i] = a[i] ? 1 : 0;
        for (int i = 0; i < b.length; i++)
          bReal[i] = b[i] ? 1 : 0;
        fft(aReal, aImaginary, false);
        fft(bReal, bImaginary, false);
        for (int i = 0; i < resultSize; i++) {
          double real = aReal[i] * bReal[i] - aImaginary[i] * bImaginary[i];
          aImaginary[i] = aImaginary[i] * bReal[i] + bImaginary[i] * aReal[i];
          aReal[i] = real;
        }
        fft(aReal, aImaginary, true);
        boolean[] result = new boolean[resultSize];
        for (int i = 0; i < resultSize; i++)
          result[i] = ((int) (aReal[i] + 0.5) >= 1);
        int okId = resultSize - 1;
        while (okId >= 0 && result[okId] == false) okId--;
        okId++;
        boolean[] nResult = new boolean[okId];
        for (int i = 0; i < okId; i++)
          nResult[i] = result[i];
        return nResult;
      }

      public boolean[] bpow(boolean[] a, int k) {
        if (k == 1) return a;
        if (k % 2 == 1) return multiply(a, bpow(a, k - 1));
        a = bpow(a, k / 2);
        return multiply(a, a);
      }

    }    

    public void solve(int test, Reader input, PrintWriter out)
    {
        MyScanner in = new MyScanner(input);
        
        int n = in.nextInt();
        int k = in.nextInt();
        
        boolean[] v = new boolean[1 << 10];
        
        while (n-- > 0) {
            int x;
            x = in.nextInt();
            v[x] = true;
        }
        
        FastFourierTransform foo = new FastFourierTransform();
        v = foo.bpow(v, (int) k);
        for (int i = 0; i < v.length; ++i) {
            if (v[i]) out.print(i + " ");
        }
        out.println();    
    }

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner(Reader reader) {
            br = new BufferedReader(reader);
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        
        int[] nextIntArray(int n)
        {
            int[] r = new int[n];
            for(int i = 0; i < n; i++)
                r[i] = nextInt();
            return r;
        }

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    //--------------------------------------------------------

}
