Problem:
Max Score: $250$ Points

Problem Statement

Snuke has a very long calendar. It has a grid with $n$ rows and $7$ columns. One day, he noticed that calendar has a following regularity.

The cell at the $i$-th row and $j$-th column contains the integer $7i+j-7$.

A good sub-grid is a $3 \times 3$ sub-grid and the sum of integers in this sub-grid mod $11$ is $k$.

How many good sub-grid are there? Write a program and help him.

Input

The input is given from standard input in the following format.

$n \quad k$

Output

Print the number of good sub-grid. If there are no solution exists, print 0.

Constraints

$1 \le n \le 10^9$

$0 \le k \le 10$

Subtasks

Subtask 1 [ $150$ points ]

The testcase in the subtask satisfies $1 \le n \le 100$.

Subtask 2 [ $100$ points ]

There are no additional constraints.

Sample Input 1

7 7

Sample Output 1

2

In this case, the calendar likes this matrix.

Sun.

Mon.

Tue.

Wed.

Thu.

Fri.

Sat.

Week 1

1

2

3

4

5

6

7

Week 2

8

9

10

11

12

13

14

Week 3

15

16

17

18

19

20

21

Week 4

22

23

24

25

26

27

28

Week 5

29

30

31

32

33

34

35

Week 6

36

37

38

39

40

41

42

Week 7

43

44

45

46

47

48

49

The cell at $i$-th row and $j$-th column is denoted $(i, j)$.

If upper-left is $(1, 5)$, the sum of integers is $5+6+7+12+13+14+19+20+21=117$.

If upper-left is $(3, 2)$, the sum of integers is $16+17+18+23+24+25+30+31+32=216$.

Therefore, there are 2 good sub-grids.

Sample Input 2

6 0

Sample Output 2

2

If upper-left is $(1, 3)$ or $(4, 4)$, it is a good sub-grid.

Sample Input 3

18 10

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)


n, k = [ int(v) for v in input().split() ]
mod_list = [6,4,2,0,9,7,5,3,1,10,8]
g = mod_list.index(k)
corumn_list = [ None for i in range(5) ]

for i in range(11):
    for j in range(1,6):
        if (7*i+j) % 11 == g and corumn_list[j-1] is None:
            corumn_list[j-1] = i

m = (n-3)%11
ans = (5*((n-3)//11)+sum([m >= i  for i in corumn_list]))
print(ans)