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C. Party Lemonade

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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.

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.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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