A New Year party is not a New Year party without lemonade! As usual, you are expecting a lot of guests, and buying lemonade has already become a pleasant necessity.

Your favorite store sells lemonade in bottles of n different volumes at different costs. A single bottle of type i has volume 2i - 1 liters and costs ci roubles. The number of bottles of each type in the store can be considered infinite.

You want to buy at least L liters of lemonade. How many roubles do you have to spend?

Input

The first line contains two integers n and L (1 ≤ n ≤ 30; 1 ≤ L ≤ 109) — the number of types of bottles in the store and the required amount of lemonade in liters, respectively.

The second line contains n integers c1, c2, ..., cn (1 ≤ ci ≤ 109) — the costs of bottles of different types.

Output

Output a single integer — the smallest number of roubles you have to pay in order to buy at least L liters of lemonade.

Examples

Input

4 12
20 30 70 90


Output

150


Input

4 3
10000 1000 100 10


Output

10


Input

4 3
10 100 1000 10000


Output

30


Input

5 787787787
123456789 234567890 345678901 456789012 987654321


Output

44981600785557577

Note

In the first example you should buy one 8-liter bottle for 90 roubles and two 2-liter bottles for 30 roubles each. In total you'll get 12 liters of lemonade for just 150 roubles.

In the second example, even though you need only 3 liters, it's cheaper to buy a single 8-liter bottle for 10 roubles.

In the third example it's best to buy three 1-liter bottles for 10 roubles each, getting three liters for 30 roubles.
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization("unroll-loops")
using namespace std;
template <typename T>
inline T gcd(T a, T b) {
  while (b != 0) swap(b, a %= b);
  return a;
}
void __print(long long x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char* x) { cerr << '\"' << x << '\"'; }
void __print(const string& x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V>& x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T& x) {
  long long f = 0;
  cerr << '{';
  for (auto& i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
template <class T>
bool selfmax(T& a, const T& b) {
  long long to_ret = 0;
  if (a < b) to_ret = 1;
  a = max(a, b);
  return to_ret;
}
template <class T>
bool selfmin(T& a, const T& b) {
  long long to_ret = 0;
  if (a > b) to_ret = 1;
  a = min(a, b);
  return to_ret;
}
template <typename... T>
void read(T&... args) {
  ((cin >> args), ...);
}
template <class A>
void read(vector<A>& x) {
  for (auto& a : x) read(a);
}
template <class A>
void read(vector<pair<A, A> >& x) {
  for (auto& a : x) read(a.first, a.second);
}
template <typename... T>
void read(vector<long long>& a) {
  long long n = a.size();
  for (long long i = 0; i < n; i++) cin >> a[i];
}
template <class A>
void print(vector<A>& a) {
  for (auto& x : a) cout << x << " ";
  cout << endl;
}
long long prod(long long a, long long b, long long m) {
  long long res = 0;
  while (b) {
    if (b & 1) res = (res + a) % m;
    a = (a + a) % m;
    b >>= 1;
  }
  return res;
}
long long power(long long a, long long b, long long m) {
  long long res = 1;
  while (b) {
    if (b & 1) res = prod(res, a, m);
    a = prod(a, a, m);
    b >>= 1;
  }
  return res;
}
long long dx[] = {1, 0, -1, 0};
long long dy[] = {0, 1, 0, -1};
const long long MOD = 1e9 + 7;
const long long INF = 1000000000;
const long long BIGINF = 1e12;
void solve() {
  long long n, l;
  read(n, l);
  vector<long long> c(n);
  read(c);
  vector<long long> bestprice = c;
  long long flag = 0;
  for (long long i = 0; i < n; i++) {
    for (long long j = 0; j < n; j++) {
      if (j < i) {
        long long diff = i - j;
        flag |= selfmin(bestprice[i], (long long)pow(2, diff) * (c[j]));
      } else {
        flag |= selfmin(bestprice[i], c[j]);
      }
    }
  }
  long long nn = l;
  long long ans = LLONG_MAX;
  long long pos = 0;
  for (long long i = n - 1; i >= 0; i--) {
    long long powe = 1 << i;
    if (nn > 0) {
      long long idx = (long long)log2(nn);
      long long mini = LLONG_MAX;
      if (idx + 1 < n) mini = min(mini, bestprice[idx + 1]);
      ans = min(ans, pos + mini);
    }
    if (nn >= powe) {
      long long temp = nn / powe;
      pos += bestprice[i] * temp;
      nn -= temp * powe;
    }
  }
  ans = min(ans, pos);
  cout << ans << endl;
}
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  long long t = 1;
  for (long long tt = 0; tt < t; tt++) {
    solve();
  }
}
