A8584 | Two Permutations

Rubik is very keen on number permutations.

A permutation $a$ with length $n$ is a sequence, consisting of $n$ different numbers from 1 to $n$ . Element number $i$ $(1<=i<=n)$ of this permutation will be denoted as $a_{i}$ .

Furik decided to make a present to Rubik and came up with a new problem on permutations. Furik tells Rubik two number permutations: permutation $a$ with length $n$ and permutation $b$ with length $m$ . Rubik must give an answer to the problem: how many distinct integers $d$ exist, such that sequence $c$ $(c_{1}=a_{1}+d,c_{2}=a_{2}+d,...,c_{n}=a_{n}+d)$ of length $n$ is a subsequence of $b$ .

Sequence $a$ is a subsequence of sequence $b$ , if there are such indices $i_{1},i_{2},...,i_{n}$ $(1<=i_{1}<i_{2}<...<i_{n}<=m)$ , that $a_{1}=b_{i1}$ , $a_{2}=b_{i2}$ , $...$ , $a_{n}=b_{in}$ , where $n$ is the length of sequence $a$ , and $m$ is the length of sequence $b$ .

You are given permutations $a$ and $b$ , help Rubik solve the given problem.

The first line contains two integers $n$ and $m$ $(1<=n<=m<=200000)$ — the sizes of the given permutations. The second line contains $n$ distinct integers — permutation $a$ , the third line contains $m$ distinct integers — permutation $b$ . Numbers on the lines are separated by spaces.

On a single line print the answer to the problem.