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.util.*;
import java.io.*;
public class E 
{
	
	public static void main(String[] arg) throws IOException
	{
		new E();
	}
	public E() throws IOException
	{
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt();
		int k = in.nextInt();
		long[] a = new long[1001];
		for(int i = 0; i < n; i++)
		{
			a[in.nextInt()] = 1;
		}
		a = fastexpo(a, k);
		for(int i = 0; i < a.length; i++)
		{
			if(a[i] > 0) out.print(i + " ");
		}
		in.close(); out.close();
	}
	long[] fastexpo(long[] base, long pow)
	{
		if(pow == 1) return base;
		if(pow%2 == 1) return multiply(fastexpo(base, pow-1), base);
		long[] ret = fastexpo(base, pow/2);
		ret = multiply(ret, ret);
		return ret;
	}
	class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;
		public FastScanner(InputStream in)
		{
			br = new BufferedReader(new InputStreamReader(in));
			st = new StringTokenizer("");
		}
		public String next() throws IOException
		{
			while(!st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int nextInt() throws IOException
		{
			return Integer.parseInt(next());
		}
		public void close() throws IOException
		{
			br.close();
		}
	}
	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), wLenB = Math.sin(angle);
			for (int i = 0; i < count; i += len) {
				double wA = 1, wB = 0;
				for (int j = 0; j < halfLen; j++) {
					double uA = a[i + j], 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;
			}
		}
	}
	long[] multiply(long[] a, long[] b) {
		int resultSize = Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2;
		resultSize = Math.max(resultSize, 1);
		double[] aReal = new double[resultSize], aImaginary = new double[resultSize];
		double[] bReal = new double[resultSize], 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);
		if (a == b) 
		{
			System.arraycopy(aReal, 0, bReal, 0, aReal.length);
			System.arraycopy(aImaginary, 0, bImaginary, 0, aImaginary.length);
		} 
		else 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[Math.min(1_000_001, resultSize)];
		for (int i = 0; i < result.length; i++)
		{
			result[i] = Math.round(aReal[i]) > 0 ? 1 : 0;
		}
		return result;
	}
}