Driving through the Irish countryside, one frequently sees enigmatic small grey stones sitting by the wayside, spaced about a kilometre and a half apart. As it turns out, these stones once had a purpose: they were milestones, intended to demarcate this venerable unit of measurement.</p>

Being so old and, crucially, collectible by magpies and larger scamps alike, not all of these stones have remained.

Passing by some more of these tattered markers at a constant but unknown speed, you may still be able to gain some information from their placements. For example, since you started counting you have passed exactly M remaining stones; how fast could you have been driving?

입력 형식

• One line containing two positive integers, M and N (2 ≤ M ≤ N ≤ 10³): the number of consecutive stones you noticed and the total number of stones along the road respectively.
• One line containing M distinct non-negative integers T_1..M in ascending order — the times at which you passed stones in hours (0 ≤ T_i ≤ 10¹⁵).
• One line containing N distinct non-negative integers X_1..N in ascending order — the distances along the road of each milestone (0 ≤ X_i ≤ 10¹⁵) in miles.

출력 형식

Output two lines:

• First, the number of distinct possible speeds at which the car could have been travelling.
• Second, a space-separated list of all of the possible distances between the first milestone you saw and the second milestone you saw, in increasing order.

예제 입력 1

4 12
1 2 4 5
6 8 12 18 26 28 30 34 36 37 39 40

예제 출력 1

2
1 2

예제 입력 2

5 10
1 2 3 4 5
0 1 2 3 4 5 6 7 8 9

예제 출력 2

1
1

예제 입력 3

3 6
1 2 4
11 12 15 19 24 30

예제 출력 3

0

예제 입력 4

2 3
1123456789000 1123456789007
5 8 13

예제 출력 4

2
3 5