A11520. 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?

The first line contains two integers $n$ and $L$ ( $1<=n<=30$ ; $1<=L<=10^{9}$ ) — the number of types of bottles in the store and the required amount of lemonade in liters, respectively.

The second line contains $n$ integers $c_{1},c_{2},...,c_{n}$ ( $1<=c_{i}<=10^{9}$ ) — the costs of bottles of different types.

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

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.