CF913C.Party Lemonade

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 2_i_ - 1 liters and costs c__i 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?

新年派对没有柠檬水就不算新年派对！照例，你预计会迎来大量宾客，而购买柠檬水早已成为一件令人愉快的必需之事。

你最喜爱的商店以 $ n $ 种不同容量出售柠檬水，价格各不相同。第 $ i $ 种瓶子的容量为 $ 2^{i-1} $ 升，售价为 $ c_i $ 卢布。商店中每种瓶子的数量可视为无限。

你想至少购买 $ L $ 升柠檬水。你最少需要花费多少卢布？

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 _c_1, _c_2, ..., c__n (1 ≤ c__i ≤ 109) — the costs of bottles of different types.

第一行包含两个整数 $n$ 和 $L$（$1 \leq n \leq 30$；$1 \leq L \leq 10^9$），分别表示商店中柠檬水瓶的种类数以及所需的柠檬水量（单位：升）。

第二行包含 $n$ 个整数 $c_1,\,c_2,\,...,\,c_n$（$1 \leq c_i \leq 10^9$），表示不同种类瓶子的价格。

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

输出一个整数——为购买至少 L 升柠檬水所需支付的最少卢布数。

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.

在第一个例子中，您应购买一瓶 8 升装的柠檬水（90 卢布）和两瓶 2 升装的柠檬水（每瓶 30 卢布）。总计您将获得 12 升柠檬水，仅需 150 卢布。

在第二个例子中，尽管您仅需 3 升，但购买一瓶 8 升装的柠檬水（10 卢布）更为便宜。

在第三个例子中，最佳方案是购买三瓶 1 升装的柠檬水（每瓶 10 卢布），以 30 卢布获得 3 升柠檬水。