2017 Fall Waterloo Local ACM Contest, Problem B

Vera has ~A \times B~ cards. Each card has a rank, an integer between ~0~ and ~A-1~, and a suit, an integer between ~0~ and ~B-1~. All cards are distinct. A set of five different cards is known as a hand. Each hand is in exactly one of nine categories numbered from ~1~ to ~9~. If a hand satisfies the conditions for membership in multiple categories, it is considered to be in the lowest-numbered such category. The rules for each category are:

1. Straight flush: is a Straight and a Flush.
2. Four of a kind: four of the cards have the same rank.
3. Full house: three of the cards have the same rank and the remaining two have the same rank.
4. Flush: all five cards have the same suit.
5. Straight: the ranks of the cards in increasing order are ~x, x+1, x+2, x+3, x+4~ for some integer ~x~.
6. Three of a kind: three of the cards have the same rank.
7. Two pair: two cards have the same rank and two other cards have the same rank.
8. One pair: two cards have the same rank.
9. High card: if a hand does not satisfy any other category.

Currently, Vera has two cards with ranks ~a_1, a_2~ and suits ~b_1, b_2~. Of the remaining cards, Vera will choose three more cards and form a hand with her two current cards. Compute the number of different hands formed in this way that belong in each category.

Input

Line ~1~ contains integers ~A~ and ~B~ ~(5 \le A \le 25, 1 \le B \le 4)~.

Line ~2~ contains integers ~a_1, b_1, a_2, b_2~ ~(0 \le a_1, a_2 \le A-1, 0 \le b_1, b_2 \le B-1, (a_1, b_1) \ne (a_2, b_2))~.

Output

Print one line with nine integers, the number of different hands that belong in each category in increasing order of categories (from Straight flush to High card).

Sample Input 1

5 2
1 0 3 1

Sample Output 1

0 0 0 0 8 0 12 36 0

Sample Input 2

13 4
0 0 1 0

Sample Output 2

1 2 18 164 63 308 792 7920 10332

Note

Let ~(a, b)~ denote a card with rank ~a~ and suit ~b~.

For the first example, Vera currently has cards ~(1, 0)~ and ~(3, 1)~. If she chooses additional cards ~(3, 0), (4, 0), (4, 1)~, her hand will be a Two pair as there are two cards with rank 3 and two other cards with rank 4. Note that this hand also satisfies being a One pair, but Two pair is the lower-numbered category.