Arpa and his friends are in a construction camp, their mission is to build and repair houses for poor people. Mojtaba is their commander. Totally there are $$n!$$ groups of students in camp, each group containing $$n$$ students. Camp lasts for $$\frac{n! \times (n! - 1)}{2}$$ days. Every they at 6 am Mojtaba rings the morning bell, all of the groups stand in their row. In each group, every person has an id from 1 to $$n$$, ids are unique. Also, groups are unique, i.e. there are no two groups with the same lineup. For example, if n = 3, here is the lineups:

• Group #1: 1 2 3
• Group #2: 1 3 2
• Group #3: 2 1 3
• Group #4: 2 3 1
• Group #5: 3 1 2
• Group #6: 3 2 1

After the national anthem, Mojtaba chooses 2 groups, persons with the same position and id in these two groups join each other and go for construction. Mojtaba never chooses the same pair of groups. Can you determine how many days at least $$k$$ pairs of students will go to construction till the end of camp?

In short, you need to find the number of ways to select $$2$$ distinct unordered permutations of size $$n$$ such that the permutations contain the same element on atleasy $$k$$ distinct indices . Print the answer modulo $$10^9+7$$. We don't know the number of students exactly, so print the answer for each $$n$$ from 1 to $$A$$.

Input Format

The first line contains two integers, A, k (\(1 \leq A, k \leq 2 \times 10^5\)).

Output Format

For each $$n$$ from 1 to $$A$$ print the answer.