Problem Statement

Consider the following game:

• The game is played using a row of $N$ squares and many stones.
• First, $a_i$ stones are put in Square $i(1\le i\le N)$ .
• A player can perform the following operation as many time as desired: "Select an integer $i$ such that Square $i$ contains exactly $i$ stones. Remove all the stones from Square $i$ , and add one stone to each of the $i-1$ squares from Square $1$ to Square $i-1$ ."
• The final score of the player is the total number of the stones remaining in the squares.

For a sequence $a$ of length $N$ , let $f(a)$ be the minimum score that can be obtained when the game is played on $a$ .

Find the sum of $f(a)$ over all sequences $a$ of length $N$ where each element is between $0$ and $K$ (inclusive). Since it can be extremely large, find the answer modulo $1000000007(={10}^9+7)$ .

Constraints

• $1\le N\le 100$
• $1\le K\le N$

Input

Input is given from Standard Input in the following format:

$N$ $K$

Output

Print the sum of $f(a)$ modulo $1000000007(={10}^9+7)$ .

Sample Input 1

2 2

Sample Output 1

10

There are nine sequences of length $2$ where each element is between $0$ and $2$ . For each of them, the value of $f(a)$ and how to achieve it is as follows:

• $$\begin{gathered} f( \\ 0,0 \\ ) \end{gathered}$$ : $0$ (Nothing can be done)
• $$\begin{gathered} f( \\ 0,1 \\ ) \end{gathered}$$ : $1$ (Nothing can be done)
• $$\begin{gathered} f( \\ 0,2 \\ ) \end{gathered}$$ : $0$ (Select Square $2$ , then Square $1$ )
• $$\begin{gathered} f( \\ 1,0 \\ ) \end{gathered}$$ : $0$ (Select Square $1$ )
• $$\begin{gathered} f( \\ 1,1 \\ ) \end{gathered}$$ : $1$ (Select Square $1$ )
• $$\begin{gathered} f( \\ 1,2 \\ ) \end{gathered}$$ : $0$ (Select Square $1$ , Square $2$ , then Square $1$ )
• $$\begin{gathered} f( \\ 2,0 \\ ) \end{gathered}$$ : $2$ (Nothing can be done)
• $$\begin{gathered} f( \\ 2,1 \\ ) \end{gathered}$$ : $3$ (Nothing can be done)
• $$\begin{gathered} f( \\ 2,2 \\ ) \end{gathered}$$ : $3$ (Select Square $2$ )

Sample Input 2

20 17

Sample Output 2

983853488