Consecutive Losses

India and Pakistan are playing a bilateral series of A matches. Now, you know that India won exactly B matches. We know that there are ^AC_B ways in which India could win B out of the A matches played. Here ^NC_R is the number of ways to choose R objects out of N objects. 

Having known that we want to know the number of possible results in which the maximum consecutive number of matches lost by India is exactly K.
We need to find that count for all K from 1 to A-B. Since the answer can be large, calculate it modulo 10⁹ + 7.

1 <= B < A <= 5 x 10⁵

Return an array of length A - B, the i^th element denotes the number of possible results in which maximum consecutive losses is exactly equal to i.

Since the answer can be large, calculate it modulo 10⁹ + 7.

Input 1:

  A : 5
  B : 2

Input 2:

  A : 4
  B : 1

Output 1:

  [1, 6, 3]

Output 2:

  [0, 2, 2]

Explanation 1:

  Let's denote a win by W and a defeat by L.
  So, possible number of ways in which India could win 2 out of 5 matches are-
  1.  WWLLL - Maximum 3 consecutive losses
  2.  WLWLL - Maximum 2 consecutive losses
  3.  WLLWL - Maximum 2 consecutive losses
  4.  WLLLW - Maximum 3 consecutive losses
  5.  LWWLL - Maximum 2 consecutive losses
  6.  LWLWL - Maximum 1 consecutive loss
  7.  LWLLW - Maximum 2 consecutive losses
  8.  LLWWL - Maximum 2 consecutive losses
  9.  LLWLW - Maximum 2 consecutive losses
  10. LLLWW - Maximum 3 consecutive losses

Explanation 2:

  Possible outcomes are- 
  1. WLLL - Maximum 3 consecutive losses
  2. LWLL - Maximum 2 consecutive losses
  3. LLWL - Maximum 2 consecutive losses
  4. LLLW - Maximum 3 consecutive losses