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Problems

K-permutation

K-permutation

Time limit 1 second
Memory limit 128 MiB

Let's call a permutation of n numbers 1 ... n a k - permutation if any two adjacent elements in it differ by no more than k.

Find the number of k-permutations from the numbers 1 ... n.

Input data

Two integers n, k (1kn9).

Output data

Print the number of k-permutations from the numbers 1 ... n.

Examples

Input example #1
3 1
Output example #1
2