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
#include <bits/stdc++.h>
using namespace std;
namespace fft {
struct num {
  double x, y;
  num() { x = y = 0; }
  num(double x, double y) : x(x), y(y) {}
};
inline num operator+(num a, num b) { return num(a.x + b.x, a.y + b.y); }
inline num operator-(num a, num b) { return num(a.x - b.x, a.y - b.y); }
inline num operator*(num a, num b) {
  return num(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
}
inline num conj(num a) { return num(a.x, -a.y); }
int base = 1;
vector<num> roots = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};
const double PI = acosl(-1.0);
void ensure_base(int nbase) {
  if (nbase <= base) return;
  rev.resize(1 << nbase);
  for (int i = 0; i < (1 << nbase); i++)
    rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
  roots.resize(1 << nbase);
  while (base < nbase) {
    double angle = 2 * PI / (1 << (base + 1));
    for (int i = 1 << (base - 1); i < (1 << base); i++) {
      roots[i << 1] = roots[i];
      double angle_i = angle * (2 * i + 1 - (1 << base));
      roots[(i << 1) + 1] = num(cos(angle_i), sin(angle_i));
    }
    base++;
  }
}
void fft(vector<num> &a, int n = -1) {
  if (n == -1) n = a.size();
  assert((n & (n - 1)) == 0);
  int zeros = __builtin_ctz(n);
  ensure_base(zeros);
  int shift = base - zeros;
  for (int i = 0; i < n; i++)
    if (i < (rev[i] >> shift)) swap(a[i], a[rev[i] >> shift]);
  for (int k = 1; k < n; k <<= 1) {
    for (int i = 0; i < n; i += 2 * k) {
      for (int j = 0; j < k; j++) {
        num z = a[i + j + k] * roots[j + k];
        a[i + j + k] = a[i + j] - z;
        a[i + j] = a[i + j] + z;
      }
    }
  }
}
vector<num> fa, fb;
vector<int> multiply(vector<int> &a, vector<int> &b) {
  int need = a.size() + b.size() - 1;
  int nbase = 0;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int)fa.size()) fa.resize(sz);
  for (int i = 0; i < sz; i++) {
    int x = (i < (int)a.size() ? a[i] : 0);
    int y = (i < (int)b.size() ? b[i] : 0);
    fa[i] = num(x, y);
  }
  fft(fa, sz);
  num r(0, -0.25 / sz);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num z = (fa[j] * fa[j] - conj(fa[i] * fa[i])) * r;
    if (i != j) fa[j] = (fa[i] * fa[i] - conj(fa[j] * fa[j])) * r;
    fa[i] = z;
  }
  fft(fa, sz);
  vector<int> res(need);
  for (int i = 0; i < need; i++) res[i] = fa[i].x + 0.5;
  return res;
}
vector<int> multiply_mod(vector<int> &a, vector<int> &b, int m, int eq = 0) {
  int need = a.size() + b.size() - 1;
  int nbase = 0;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int)fa.size()) fa.resize(sz);
  for (int i = 0; i < (int)a.size(); i++) {
    int x = (a[i] % m + m) % m;
    fa[i] = num(x & ((1 << 15) - 1), x >> 15);
  }
  fill(fa.begin() + a.size(), fa.begin() + sz, num{0, 0});
  fft(fa, sz);
  if (sz > (int)fb.size()) fb.resize(sz);
  if (eq)
    copy(fa.begin(), fa.begin() + sz, fb.begin());
  else {
    for (int i = 0; i < (int)b.size(); i++) {
      int x = (b[i] % m + m) % m;
      fb[i] = num(x & ((1 << 15) - 1), x >> 15);
    }
    fill(fb.begin() + b.size(), fb.begin() + sz, num{0, 0});
    fft(fb, sz);
  }
  double ratio = 0.25 / sz;
  num r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num a1 = (fa[i] + conj(fa[j]));
    num a2 = (fa[i] - conj(fa[j])) * r2;
    num b1 = (fb[i] + conj(fb[j])) * r3;
    num b2 = (fb[i] - conj(fb[j])) * r4;
    if (i != j) {
      num c1 = (fa[j] + conj(fa[i]));
      num c2 = (fa[j] - conj(fa[i])) * r2;
      num d1 = (fb[j] + conj(fb[i])) * r3;
      num d2 = (fb[j] - conj(fb[i])) * r4;
      fa[i] = c1 * d1 + c2 * d2 * r5;
      fb[i] = c1 * d2 + c2 * d1;
    }
    fa[j] = a1 * b1 + a2 * b2 * r5;
    fb[j] = a1 * b2 + a2 * b1;
  }
  fft(fa, sz);
  fft(fb, sz);
  vector<int> res(need);
  for (int i = 0; i < need; i++) {
    long long aa = fa[i].x + 0.5;
    long long bb = fb[i].x + 0.5;
    long long cc = fa[i].y + 0.5;
    res[i] = (aa + ((bb % m) << 15) + ((cc % m) << 30)) % m;
  }
  return res;
}
vector<int> square_mod(vector<int> &a, int m) {
  return multiply_mod(a, a, m, 1);
}
vector<int> power(vector<int> &v, int p) {
  vector<int> r = v;
  p--;
  while (p) {
    if (p & 1) {
      r = multiply(r, v);
      for (auto &x : r)
        if (x > 1) x = 1;
    }
    v = multiply(v, v);
    for (auto &x : v)
      if (x > 1) x = 1;
    p >>= 1;
  }
  return r;
}
};  // namespace fft
int main() {
  int n, k;
  cin >> n >> k;
  vector<int> a(1001, 0);
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    a[x] = 1;
  }
  vector<int> v = fft::power(a, k);
  for (int i = 1; i < v.size(); i++)
    if (v[i] > 0) cout << i << ' ';
  cout << '\n';
  return 0;
}
