Solve the programming task below in a Python markdown code block.
You are given an array A = [1, 2, 3, ..., n]:     

How many sequences ($S_{1}$) can you get after exact k adjacent swaps on A? 

How many sequences ($S_{2}$) can you get after at most k swaps on A?  

An adjacent swap can be made between two elements of the Array A, A[i] and A[i+1] or A[i] and A[i-1]. 

A swap otherwise can be between any two elements of the array A[i] and A[j] ∀ 1 ≤ i, j ≤ N, i ≠ j.

Input Format

First and only line contains n and k separated by space.    

Constraints

1 ≤ n ≤ 2500 

1 ≤ k ≤ 2500      

Output Format

Output $S_{1}$ % MOD and $S_{2} $% MOD in one line, where MOD = 1000000007.    

Sample Input
3 2

Sample Output
3 6

Explanation
Original array: [1, 2, 3]
1. After 2 adjacent swaps:
We can get [1, 2, 3], [2, 3, 1], [3, 1, 2] ==> S1 == 3

2. After at most 2 swaps:
1) After 0 swap: [1, 2, 3]
2) After 1 swap: [2, 1, 3], [3, 2, 1], [1, 3, 2].
3) After 2 swaps: [1, 2, 3], [2, 3, 1], [3, 1, 2]
==> S2 == 6