The Number of N-k-special Sets

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Problem

A set XX of natural numbers is called nn-kk-special when all of the following hold:

  • every element xXx \in X satisfies 1xn1 \le x \le n,
  • the sum of all elements of XX is strictly greater than kk,
  • XX contains no pair of consecutive natural numbers, that is, no two elements differ by exactly 11.

Given two natural numbers nn and kk, write a program that computes the number of nn-kk-special sets.

Input

The first line contains two natural numbers nn and kk separated by a single space, with 1n1001 \le n \le 100 and 0k4000 \le k \le 400.

Output

Print one non-negative integer: the number of nn-kk-special sets for the given nn and kk.