There are \(n\) stones in a row from left to right. You are standing on the first stone. From every step from stone number \(i\), you can jump at most \(k\) stones further (\(i + 1,\ i + 2,\ \dots,\ i + k\)). You cannot jump over stone number \(n\). How many ways are there to travel to stone number \(n\)?

Input format

First line: \(n\) and \(k\)

Output format

Print the answer modulo \(10^9+7\).