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.
input1 = raw_input()
input1_args = input1.split(' ')
num_bottles = long(input1_args[0])
num_lemonade = long(input1_args[1])
str_binary = "{0:b}".format(num_lemonade)

input2 = raw_input()
str_costs = input2.split(' ')
costs = []
for str_cost in str_costs:
    costs.append(long(str_cost))

str_zeros = ""
for i in range(len(str_costs) - len(str_binary)):
    str_zeros += "0"
str_binary = str_zeros + str_binary

alt_costs = [costs[0]]
for i in range(1, len(costs)):
    if alt_costs[i - 1] * 2 < costs[i]:
        alt_costs.append(alt_costs[i - 1] * 2)
    else:
        alt_costs.append(costs[i])

for i in range(len(costs), len(str_binary)):
    alt_costs.append(alt_costs[i-1] * 2)
sums = []
index = 0
for i in range(len(str_binary) - 1, -1, -1):
    if str_binary[i] == "1":
        sums.append(alt_costs[index])
    else:
        sums.append(0)
    index += 1
    
total_sum = 0
index = 0
for sm in sums:
    if index < len(costs) and total_sum > costs[index]:
        total_sum = costs[index]
    total_sum += sm
    index += 1

print(total_sum)