The floor of your house consists of five rows of square tiles and each row is $N$ tiles long.

You must paint the whole floor by using at most four colors such that the total number of $i^{th}$ ($1 \le i \le 4$) colored tiles in any two consecutive columns of the floor should not exceed $K$. Determine the number of ways in which you can paint the floor. 
Since the answer can be very large, compute it modulo $10^9+7$.

Note: The floor should be completely painted. If there is no way to paint the floor completely, then print $0$.

Input format

• First line: Two space-separated integers $N$ and $K$

Output format

Print a single integer that denotes the number of ways to paint the floor completely.

Constraints

$1 \le N \le 1000\\ 1 \le K \le 10$