Description

Original source: NOIP 2006 Senior Division

Let $r$ be a $2^k$-based number that satisfies the following conditions:

• $r$ must be at least a 2-digit number in base $2^k$.
• As a $2^k$-based number, every digit of $r$ (except the last one) is strictly less than the digit immediately to its right.
• After converting $r$ to a binary number $q$, the total number of bits in $q$ does not exceed $w$.

Here, the positive integers $k$ and $w$ are given in advance.

Question: How many distinct $r$ satisfy the above conditions?

Input Format

The input consists of a single line with two positive integers $k$ and $w$.

Output Format

The output is a single line containing a positive integer, which is the result of the calculation—the number of distinct $r$ that satisfy the conditions (expressed in decimal, with the highest digit not being zero and no additional characters such as spaces, line breaks, or commas inserted between digits).

Note: The resulting positive integer may be very large but will not exceed 200 digits.

Sample 1

3 7

36

Data Range and Hint

For all data, $1\le k\le 9,k\lt w\le 3\times 10^4$.