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.
(n, L) = map(int, input().split())

lst = []
for x in input().split():
    lst.append(int(x))

lst.extend([10 ** 20] * (31 - n))
for x in range(len(lst) - 1):
    lst[x + 1] = min(lst[x + 1], 2 * lst[x])

s = bin(L)[2:]
s = s[::-1]
price = 0
for x in range(len(s)):
    price += int(s[x]) * lst[x]

for x in range(len(lst)):
    if x >= len(s):
        price = min(price, lst[x])
    else:
        if s[x] == '0':
            p = lst[x]
            for y in range(x + 1, len(s)):
                p += int(s[y]) * lst[y]
            price = min(price, p)

print(price)
