Minimum Final Value in Liqiu's Array

In this problem, Liqiu has an array \(a\) of length \(n\) consisting of positive integers. The array satisfies the following property: for every \(i\) from 2 to \(n\),
\[ a_i = \sum_{j=1}^{i-1} a_j, \]that is, every element except the first one is equal to the sum of all previous elements.

For example, the array \([1, 1, 2, 4, 8, 16]\) is valid because:

• \(a_2 = 1 = a_1\),
• \(a_3 = 1+1 = 2\),
• \(a_4 = 1+1+2 = 4\),
• \(a_5 = 1+1+2+4 = 8\),
• \(a_6 = 1+1+2+4+8 = 16\).

Now, Liqiu tells Qiuli that a given positive integer \(x\) appears somewhere in the array. Qiuli wants to determine the minimum possible value of the last element \(a_n\) among all arrays satisfying the above conditions and containing \(x\) as one of the elements.

Observation: If we set the first element \(a_1 = k\) (for some positive integer \(k\)), then the array is uniquely determined as follows:

• \(a_1 = k\),
• \(a_2 = k\),
• \(a_3 = 2k\),
• \(a_4 = 4k\),
• ... ,
• \(a_i = 2^{i-2} \times k \) for \(i\ge 2\).

Thus, if \(x\) is chosen to be the \(i\)-th element, then we must have:

[ a_i = 2^{i-2} \times k = x \quad (\text{for } i \ge 2), ]

which implies \(k = \frac{x}{2^{i-2}}\) (and it must be a positive integer). The final element is

[ a_n = 2^{n-2} \times k = 2^{n-2} \times \frac{x}{2^{i-2}} = 2^{n-i} \times x. ]

We want to minimize \(a_n\) among all valid choices of \(i\) (where \(1 \le i \le n\) with the convention that when \(i=1\), we take \(x=a_1\) and then \(a_n = 2^{n-2} \times x\) if \(n \ge 2\), or \(a_n=x\) when \(n=1\)). Notice that potentially choosing a larger \(i\) (i.e. more division by a power of 2) can lead to a smaller value of \(a_n\) provided the divisibility condition is met.

Your task is to compute the minimum possible value of \(a_n\) given \(n\) and \(x\).

inputFormat

The input consists of a single line containing two positive integers \(n\) and \(x\) where \(n\) is the length of the array and \(x\) is the value that appears in the array.

outputFormat

Output a single integer, which is the minimum possible value of \(a_n\) under the given conditions.

sample

6 1

16