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?

Input

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

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

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.