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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class thiefs {
	
	public static void main(String[] args) {
		FastScanner in = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
				
		int n = in.nextInt();
		int k = in.nextInt();
		int nextPow = Integer.highestOneBit(1000) << 2;
		
		long[] poly = new long[nextPow];
		for(int i = 0; i < n; ++i) {
			int cost = in.nextInt();
			poly[cost] = 1;
		}
		
		long[] ans = new long[nextPow];
		ans[0] = 1;
		while(k > 0) {
			if(k % 2 == 0) {
				k /= 2;
				poly = FFT.multiply(poly, poly);
				for(int i = 0; i < poly.length; ++i) if(poly[i] > 1) poly[i] = 1;
			} else {
				--k;
				long[] kk = new long[poly.length];
				for(int i = 0; i < ans.length; ++i) {
					kk[i] = ans[i];
				}
				ans = FFT.multiply(poly, kk);
				for(int i = 0; i < ans.length; ++i) if(ans[i] > 1) ans[i] = 1;
			}
		}
		
		List<Integer> values = new ArrayList<>();
		for(int i = 0; i < ans.length; ++i) {
			if(ans[i] == 0) continue;
			values.add(i);
		}
		
		for(long i : values) {
			out.print(i + " ");
		}
		out.println();
		
		out.close();
	}
	
	public static class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(String s)
		{
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}

		public FastScanner()
		{
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String nextToken()
		{
			while (st == null || !st.hasMoreElements())
			{
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt()
		{
			return Integer.parseInt(nextToken());
		}

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

		double nextDouble()
		{
			return Double.parseDouble(nextToken());
		}
		
		String next()
		{
			return nextToken();
		}
	}
	
	static class FFT {
		
		public static void fft(double[] a, double[] b, boolean invert) {
	        int n = a.length;
	        int shift = 32 - Integer.numberOfTrailingZeros(n);
	        for (int i = 1; i < n; i++) {
	            int j = Integer.reverse(i << shift);
	            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 <= n; len <<= 1) {
	            int halfLen = len >> 1;
	            double angle = 2 * Math.PI / len * (invert ? -1 : 1);
	            double wLenA = Math.cos(angle);
	            double wLenB = Math.sin(angle);
	            for (int i = 0; i < n; 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 < n; i++) {
	                a[i] /= n;
	                b[i] /= n;
	            }
	        }
	    }
	
	    public static long[] multiply(long[] a, long[] b) {
	        int resultSize = Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2;
	        resultSize = Math.max(resultSize, 2);
	        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];
	        for (int i = 0; i < b.length; i++)
	            bReal[i] = b[i];
	        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);
	        long[] result = new long[resultSize];
	        for (int i = 0; i < resultSize; i++) {
	            result[i] = Math.round(aReal[i]);
	        }
	        return result;
	    }
		
	}
}
