Score : $500$ points

Problem Statement

You are given a sequence of $N-1$ integers $S = (S_1, S_2, \ldots, S_{N-1})$, and $M$ distinct integers $X_1, X_2, \ldots, X_M$, which are called lucky numbers.

A sequence of $N$ integers $A = (A_1, A_2, \ldots, A_N)$ satisfying the following condition is called a good sequence.

$A_i + A_{i+1} = S_i$ holds for every $i = 1, 2, \ldots, N-1$.

Find the maximum possible number of terms that are lucky numbers in a good sequence $A$, that is, the maximum possible number of integers $i$ between $1$ and $N$ such that $A_i \in \lbrace X_1, X_2, \ldots, X_M \rbrace$.

Constraints

• $2 \leq N \leq 10^5$
• $1 \leq M \leq 10$
• $-10^9 \leq S_i \leq 10^9$
• $-10^9 \leq X_i \leq 10^9$
• $X_1 \lt X_2 \lt \cdots \lt X_M$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$S_1$ $S_2$ $\ldots$ $S_{N-1}$

$X_1$ $X_2$ $\ldots$ $X_M$

Output

Print the maximum possible number of terms that are lucky numbers in a good sequence $A$.

9 2
2 3 3 4 -4 -7 -4 -1
-1 5

4

A good sequence $A = (3, -1, 4, -1, 5, -9, 2, -6, 5)$ contains four terms that are lucky numbers: $A_2, A_4, A_5, A_9$, which is the maximum possible count.

20 10
-183260318 206417795 409343217 238245886 138964265 -415224774 -499400499 -313180261 283784093 498751662 668946791 965735441 382033304 177367159 31017484 27914238 757966050 878978971 73210901
-470019195 -379631053 -287722161 -231146414 -84796739 328710269 355719851 416979387 431167199 498905398

8