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 \leq i \leq 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 \leq N \leq 100
• 1 \leq K \leq N

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:

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

Sample Input 2

20 17

Sample Output 2

983853488