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.*;
import java.util.*;

public class Main{
	static int maxn=2000000,MOD=1009;
	static double[] wR = new double[maxn],
            wI = new double[maxn],
            rR = new double[maxn],
            rI = new double[maxn],
            aR = new double[maxn],
            aI = new double[maxn];
	static int n, k, lastk = -1, dp[] = new int[maxn];
 
    static void fft(boolean inv) {
        if (lastk != k) {
            lastk = k;
            dp[0] = 0;
            for (int i = 1, g = -1; i < n; i++) {
                if ((i & (i - 1)) == 0) {
                    g++;
                }
                dp[i] = dp[i ^ (1 << g)] ^ (1 << (k - 1 - g));
            }
            wR[1] = 1;
            wI[1] = 0;
            for (int t = 0; t < k - 1; t++) {
                double a = Math.PI / n * (1 << (k - 1 - t));
                double curR = Math.cos(a), curI = Math.sin(a);
                int p2 = (1 << t), p3 = p2 * 2;
                for (int j = p2, k = j * 2; j < p3; j++, k += 2) {
                    wR[k] = wR[j];
                    wI[k] = wI[j];
                    wR[k + 1] = wR[j] * curR - wI[j] * curI;
                    wI[k + 1] = wR[j] * curI + wI[j] * curR;
                }
            }
        }
        for (int i = 0; i < n; i++) {
            int d = dp[i];
            if (i < d) {
                double tmp = aR[i];
                aR[i] = aR[d];
                aR[d] = tmp;
                tmp = aI[i];
                aI[i] = aI[d];
                aI[d] = tmp;
            }
        }
        if (inv) {
            for (int i = 0; i < n; i++) {
                aI[i] = -aI[i];
            }
        }
        for (int len = 1; len < n; len <<= 1) {
            for (int i = 0; i < n; i += len) {
                int wit = len;
                for (int it = 0, j = i + len; it < len; it++, i++, j++) {
                    double tmpR = aR[j] * wR[wit] - aI[j] * wI[wit];
                    double tmpI = aR[j] * wI[wit] + aI[j] * wR[wit];
                    wit++;
                    aR[j] = aR[i] - tmpR;
                    aI[j] = aI[i] - tmpI;
                    aR[i] += tmpR;
                    aI[i] += tmpI;
                }
            }
        }
    }
 
    static long[] multiply(long[] a, long[] b) {
        int na = a.length, nb = b.length;
        for (k = 0, n = 1; n < na + nb - 1; n <<= 1, k++) {
        }
        for (int i = 0; i < n; ++i) {
            aR[i] = i < na ? a[i] : 0;
            aI[i] = i < nb ? b[i] : 0;
        }
        fft(false);
        aR[n] = aR[0];
        aI[n] = aI[0];
        double q = -1.0 / n / 4.0;
        for (int i = 0; i <= n - i; ++i) {
            double tmpR = aR[i] * aR[i] - aI[i] * aI[i];
            double tmpI = aR[i] * aI[i] * 2;
            tmpR -= aR[n - i] * aR[n - i] - aI[n - i] * aI[n - i];
            tmpI -= aR[n - i] * aI[n - i] * -2;
            aR[i] = -tmpI * q;
            aI[i] = tmpR * q;
            aR[n - i] = aR[i];
            aI[n - i] = -aI[i];
        }
	    fft(true);
	    long[] ans = new long[n = na + nb - 1]; // ONLY MOD IF NEEDED
		for (int i = 0; i < n; i++) {
		    ans[i] = Math.round(aR[i]);
		}
		return ans;
	}
    static long[] pow(long[]poly,int pow) {
    	if(pow==1)return poly;
    	long[]res;
    	if((pow&1)==1) {
    		res=multiply(pow(poly, pow-1), poly);
    	}
    	else {
    		long[]x=pow(poly, pow>>1);
    		res=multiply(x, x);
    	}
    	long[]ans=new long[Math.min(1000001, res.length)];
    	for(int i=0;i<ans.length;i++) {
    		ans[i]=Math.min(res[i], 1);
    	}
    	return ans;
    }
	static void main() throws Exception{
		int n=sc.nextInt(),k=sc.nextInt();
		long[]poly=new long[1001];
		while(n-->0) {
			poly[sc.nextInt()]++;
		}
		for(int i=0;i<poly.length;i++) {
			poly[i]=Math.min(poly[i], 1);
		}
		long[]ans=pow(poly, k);
		for(int i=0;i<ans.length;i++) {
			if(ans[i]>0) {
				pw.print(i+" ");
			}
		}
		pw.println();
	}
    public static void main(String[] args) throws Exception{
        sc=new MScanner(System.in);
        pw = new PrintWriter(System.out);
        int tc=1;
//        tc=sc.nextInt();
        for(int i=1;i<=tc;i++) {
//            pw.printf("Case %d:\n", i);
            main();
        }
        pw.flush();
    }
    static PrintWriter pw;
    static MScanner sc;
    static class MScanner {
        StringTokenizer st;
        BufferedReader br;
        public MScanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }
     
        public MScanner(String file) throws Exception {
            br = new BufferedReader(new FileReader(file));
        }
     
        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
        public int[] intArr(int n) throws IOException {
            int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
            return in;
        }
        public long[] longArr(int n) throws IOException {
            long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
            return in;
        }
        public int[] intSortedArr(int n) throws IOException {
            int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
            shuffle(in);
            Arrays.sort(in);
            return in;
        }
        public long[] longSortedArr(int n) throws IOException {
            long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
            shuffle(in);
            Arrays.sort(in);
            return in;
        }
        public Integer[] IntegerArr(int n) throws IOException {
            Integer[]in=new Integer[n];for(int i=0;i<n;i++)in[i]=nextInt();
            return in;
        }
        public Long[] LongArr(int n) throws IOException {
            Long[]in=new Long[n];for(int i=0;i<n;i++)in[i]=nextLong();
            return in;
        }
        public String nextLine() throws IOException {
            return br.readLine();
        }
     
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
     
        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
     
        public char nextChar() throws IOException {
            return next().charAt(0);
        }
     
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
     
        public boolean ready() throws IOException {
            return br.ready();
        }
     
        public void waitForInput() throws InterruptedException {
            Thread.sleep(3000);
        }
        
    }
    static void shuffle(int[]in) {
        for(int i=0;i<in.length;i++) {
            int idx=(int)(Math.random()*in.length);
            int tmp=in[i];
            in[i]=in[idx];
            in[idx]=tmp;
        }
    }
    static void shuffle(long[]in) {
        for(int i=0;i<in.length;i++) {
            int idx=(int)(Math.random()*in.length);
            long tmp=in[i];
            in[i]=in[idx];
            in[idx]=tmp;
        }
    }
}