Description

Given n and m, calculate the sum of the incremental multiplication formulas:

$$ f(n, m)=\sum_{i=1}^{n}\prod_{j=i}^{i+m-1}j $$

Input

No more than 50 test cases. Each case one line, including integer n and m.

1 ≤ n, m ≤ 10⁶.

Output

For each test case, output the result of f(n, m) modulo 10⁹ + 7.

2 2
98 3

8
24497550