#include <bits/stdc++.h>
using namespace std;
using pii = pair<int, int>;
const int MOD = 1000000007;
const int INF = 2000000000;
const long long DESPACITO = 1000000000000000000;
namespace minmax {
template <class T>
T max(T&& A) {
  return A;
}
template <class T>
T min(T&& A) {
  return A;
}
template <class T>
T max(T&& A, T&& B) {
  return A > B ? A : B;
}
template <class T>
T chmin2(T&& A, T&& B) {
  return A < B ? A : B;
}
template <class T, class... Ts>
T max(T&& A, Ts&&... ts) {
  T B = max(ts...);
  return A > B ? A : B;
}
template <class T, class... Ts>
T min(T&& A, Ts&&... ts) {
  T B = min(ts...);
  return A < B ? A : B;
}
template <class T, class... Ts>
T chmax(T&& A, Ts&&... ts) {
  A = max(A, ts...);
  return A;
}
template <class T, class... Ts>
T chmin(T&& A, Ts&&... ts) {
  A = min(A, ts...);
  return A;
}
template <class T1, class T2>
void chmin2(T1&& A, T2&& Aa, T1&& B, T2&& Bb) {
  if (B < A) A = B, Aa = Bb;
}
template <class T1, class T2>
void chmax2(T1&& A, T2&& Aa, T1&& B, T2&& Bb) {
  if (B > A) A = B, Aa = Bb;
}
}  // namespace minmax
namespace input {
template <class T>
void re(T&& Xx) {
  cin >> Xx;
}
template <class T1, class T2>
void re(pair<T1, T2>& Pp) {
  re(Pp.first);
  re(Pp.second);
}
template <class T>
void re(vector<T>& Aa) {
  for (int i = 0; i < (int)(Aa).size(); i++) re(Aa[i]);
}
template <class T1, class T2>
void rea(T1&& Aa, T2 t) {
  for (int i = 0; i < t; i++) re(Aa[i]);
}
template <class T1, class T2, class... Ts>
void rea(T1&& Aa, T2 t, Ts&&... ts) {
  rea(Aa, t);
  rea(ts...);
}
template <class T1, class T2>
void rea1(T1&& Aa, T2 t) {
  for (int i = 1; i <= t; i++) re(Aa[i]);
}
template <class T1, class T2, class... Ts>
void rea1(T1&& Aa, T2 t, Ts&... ts) {
  rea1(Aa, t);
  rea1(ts...);
}
template <class T, class... Ts>
void re(T&& t, Ts&... ts) {
  re(t);
  re(ts...);
}
}  // namespace input
namespace output {
void pr(int32_t Xx) { cout << Xx; }
void pr(bool Xx) { cout << Xx; }
void pr(long long Xx) { cout << Xx; }
void pr(long long unsigned Xx) { cout << Xx; }
void pr(double Xx) { cout << Xx; }
void pr(char Xx) { cout << Xx; }
void pr(const string& Xx) { cout << Xx; }
void pr(const char* Xx) { cout << Xx; }
void pr(const char* Xx, size_t len) { cout << string(Xx, len); }
void ps() { cout << "\n"; }
void pn() {}
void pw() { pr(" "); }
void pc() {
  pr("]");
  ps();
}
template <class T1, class T2>
void pr(const pair<T1, T2>& Xx) {
  pr(Xx.first);
  pw();
  pr(Xx.second);
}
template <class T>
void pr(const T&);
bool parse(const char* t) {
  if (t == "\n") return true;
  return false;
}
template <class T>
bool parse(T&& t) {
  return false;
}
template <class T1, class T2>
bool parsepair(const pair<T1, T2>& Xx) {
  return true;
}
template <class T>
bool parsepair(T&& t) {
  return false;
}
template <class T1, class T2>
void psa(T1&& Aa, T2 t) {
  for (int i = 0; i < t; i++) pr(Aa[i]), pw();
  ps();
}
template <class T1, class T2>
void pna(T1&& Aa, T2 t) {
  for (int i = 0; i < t; i++) pr(Aa[i]), ps();
}
template <class T1, class T2>
void psa2(T1&& Aa, T2 t1, T2 t2) {
  for (int i = 0; i < t1; i++) {
    for (int j = 0; j < t2; j++) pr(Aa[i][j]), pw();
    ps();
  }
}
template <class T>
void pr(const T& Xx) {
  if (!(int)(Xx).size()) return;
  bool fst = 1;
  bool op = 0;
  if (parsepair(*Xx.begin())) op = 1;
  for (const auto& Aa : Xx) {
    if (!fst) pw();
    if (op) pr("{");
    pr(Aa), fst = 0;
    if (op) pr("}");
  }
}
template <class T, class... Ts>
void pr(const T& t, const Ts&... ts) {
  pr(t);
  pr(ts...);
}
template <class T, class... Ts>
void ps(const T& t, const Ts&... ts) {
  pr(t);
  if (sizeof...(ts)) {
    if (!parse(t)) pw();
  }
  ps(ts...);
}
template <class T>
void pn(const T& t) {
  for (const auto& Aa : t) ps(Aa);
}
template <class T, class... Ts>
void pw(const T& t, const Ts&... ts) {
  pr(t);
  if (sizeof...(ts)) pw();
  pw(ts...);
}
template <class T, class... Ts>
void pc(const T& t, const Ts&... ts) {
  bool op = 0;
  if (parsepair(t)) op = 1;
  if (op) pr("{");
  pr(t);
  if (op) pr("}");
  if (sizeof...(ts)) pr(", ");
  pc(ts...);
}
namespace trace {
template <class T1, class T2>
void __f(const char* name, const T1& Xx, const T2& y) {
  pr("[", y, "] = ");
  ps(Xx);
}
template <class T1, class T2, class... Ts>
void __f(const char* name, const T1& Xx, const T2& y, const Ts&... rest) {
  const char* open = strchr(name, '[');
  pr("[", y, "]");
  __f(open + 1, Xx, rest...);
}
template <class T1, class T2, class... Ts>
void __f0(const char* name, const T1& Xx, const T2& y, const Ts&... rest) {
  const char* open = strchr(name, '[');
  pr(name, size_t(open - name));
  __f(name, Xx, y, rest...);
}
template <class T>
void __fn(int n, const char* name, const T& Xx) {
  for (int i = 0; i < n; i++) pr(name), __f(name, Xx[i], i);
}
}  // namespace trace
}  // namespace output
using namespace minmax;
using namespace input;
using namespace output;
using namespace output::trace;
const int N = 2e5 + 5;
vector<int> a, b;
vector<int> generate_pi(vector<int>& s) {
  int i, n = (int)(s).size();
  vector<int> pi(n);
  for (i = 1; i < n; i++) {
    int p = pi[i - 1];
    while (p and s[i] != s[p]) p = pi[p - 1];
    pi[i] = p + (s[i] == s[p]);
  }
  return pi;
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int i, n, m, ans = 0;
  re(n, m);
  a.resize(n);
  b.resize(m);
  re(a, b);
  vector<int> s;
  for (i = 1; i < m; i++) s.emplace_back(b[i] - b[i - 1]);
  s.emplace_back(INF);
  for (i = 1; i < n; i++) s.emplace_back(a[i] - a[i - 1]);
  auto pi = generate_pi(s);
  for (auto& x : pi)
    if (x == m - 1) ans++;
  ps(ans);
  return 0;
}

### Prompt

In CPP, your task is to solve the following problem:

Polar bears Menshykov and Uslada from the zoo of St. Petersburg and elephant Horace from the zoo of Kiev got hold of lots of wooden cubes somewhere. They started making cube towers by placing the cubes one on top of the other. They defined multiple towers standing in a line as a wall. A wall can consist of towers of different heights.

Horace was the first to finish making his wall. He called his wall an elephant. The wall consists of w towers. The bears also finished making their wall but they didn't give it a name. Their wall consists of n towers. Horace looked at the bears' tower and wondered: in how many parts of the wall can he "see an elephant"? He can "see an elephant" on a segment of w contiguous towers if the heights of the towers on the segment match as a sequence the heights of the towers in Horace's wall. In order to see as many elephants as possible, Horace can raise and lower his wall. He even can lower the wall below the ground level (see the pictures to the samples for clarification).

Your task is to count the number of segments where Horace can "see an elephant".

Input

The first line contains two integers n and w (1 ≤ n, w ≤ 2·105) — the number of towers in the bears' and the elephant's walls correspondingly. The second line contains n integers ai (1 ≤ ai ≤ 109) — the heights of the towers in the bears' wall. The third line contains w integers bi (1 ≤ bi ≤ 109) — the heights of the towers in the elephant's wall.

Output

Print the number of segments in the bears' wall where Horace can "see an elephant".

Examples

Input

13 5
2 4 5 5 4 3 2 2 2 3 3 2 1
3 4 4 3 2


Output

2

Note

The picture to the left shows Horace's wall from the sample, the picture to the right shows the bears' wall. The segments where Horace can "see an elephant" are in gray.

<image>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using pii = pair<int, int>;
const int MOD = 1000000007;
const int INF = 2000000000;
const long long DESPACITO = 1000000000000000000;
namespace minmax {
template <class T>
T max(T&& A) {
  return A;
}
template <class T>
T min(T&& A) {
  return A;
}
template <class T>
T max(T&& A, T&& B) {
  return A > B ? A : B;
}
template <class T>
T chmin2(T&& A, T&& B) {
  return A < B ? A : B;
}
template <class T, class... Ts>
T max(T&& A, Ts&&... ts) {
  T B = max(ts...);
  return A > B ? A : B;
}
template <class T, class... Ts>
T min(T&& A, Ts&&... ts) {
  T B = min(ts...);
  return A < B ? A : B;
}
template <class T, class... Ts>
T chmax(T&& A, Ts&&... ts) {
  A = max(A, ts...);
  return A;
}
template <class T, class... Ts>
T chmin(T&& A, Ts&&... ts) {
  A = min(A, ts...);
  return A;
}
template <class T1, class T2>
void chmin2(T1&& A, T2&& Aa, T1&& B, T2&& Bb) {
  if (B < A) A = B, Aa = Bb;
}
template <class T1, class T2>
void chmax2(T1&& A, T2&& Aa, T1&& B, T2&& Bb) {
  if (B > A) A = B, Aa = Bb;
}
}  // namespace minmax
namespace input {
template <class T>
void re(T&& Xx) {
  cin >> Xx;
}
template <class T1, class T2>
void re(pair<T1, T2>& Pp) {
  re(Pp.first);
  re(Pp.second);
}
template <class T>
void re(vector<T>& Aa) {
  for (int i = 0; i < (int)(Aa).size(); i++) re(Aa[i]);
}
template <class T1, class T2>
void rea(T1&& Aa, T2 t) {
  for (int i = 0; i < t; i++) re(Aa[i]);
}
template <class T1, class T2, class... Ts>
void rea(T1&& Aa, T2 t, Ts&&... ts) {
  rea(Aa, t);
  rea(ts...);
}
template <class T1, class T2>
void rea1(T1&& Aa, T2 t) {
  for (int i = 1; i <= t; i++) re(Aa[i]);
}
template <class T1, class T2, class... Ts>
void rea1(T1&& Aa, T2 t, Ts&... ts) {
  rea1(Aa, t);
  rea1(ts...);
}
template <class T, class... Ts>
void re(T&& t, Ts&... ts) {
  re(t);
  re(ts...);
}
}  // namespace input
namespace output {
void pr(int32_t Xx) { cout << Xx; }
void pr(bool Xx) { cout << Xx; }
void pr(long long Xx) { cout << Xx; }
void pr(long long unsigned Xx) { cout << Xx; }
void pr(double Xx) { cout << Xx; }
void pr(char Xx) { cout << Xx; }
void pr(const string& Xx) { cout << Xx; }
void pr(const char* Xx) { cout << Xx; }
void pr(const char* Xx, size_t len) { cout << string(Xx, len); }
void ps() { cout << "\n"; }
void pn() {}
void pw() { pr(" "); }
void pc() {
  pr("]");
  ps();
}
template <class T1, class T2>
void pr(const pair<T1, T2>& Xx) {
  pr(Xx.first);
  pw();
  pr(Xx.second);
}
template <class T>
void pr(const T&);
bool parse(const char* t) {
  if (t == "\n") return true;
  return false;
}
template <class T>
bool parse(T&& t) {
  return false;
}
template <class T1, class T2>
bool parsepair(const pair<T1, T2>& Xx) {
  return true;
}
template <class T>
bool parsepair(T&& t) {
  return false;
}
template <class T1, class T2>
void psa(T1&& Aa, T2 t) {
  for (int i = 0; i < t; i++) pr(Aa[i]), pw();
  ps();
}
template <class T1, class T2>
void pna(T1&& Aa, T2 t) {
  for (int i = 0; i < t; i++) pr(Aa[i]), ps();
}
template <class T1, class T2>
void psa2(T1&& Aa, T2 t1, T2 t2) {
  for (int i = 0; i < t1; i++) {
    for (int j = 0; j < t2; j++) pr(Aa[i][j]), pw();
    ps();
  }
}
template <class T>
void pr(const T& Xx) {
  if (!(int)(Xx).size()) return;
  bool fst = 1;
  bool op = 0;
  if (parsepair(*Xx.begin())) op = 1;
  for (const auto& Aa : Xx) {
    if (!fst) pw();
    if (op) pr("{");
    pr(Aa), fst = 0;
    if (op) pr("}");
  }
}
template <class T, class... Ts>
void pr(const T& t, const Ts&... ts) {
  pr(t);
  pr(ts...);
}
template <class T, class... Ts>
void ps(const T& t, const Ts&... ts) {
  pr(t);
  if (sizeof...(ts)) {
    if (!parse(t)) pw();
  }
  ps(ts...);
}
template <class T>
void pn(const T& t) {
  for (const auto& Aa : t) ps(Aa);
}
template <class T, class... Ts>
void pw(const T& t, const Ts&... ts) {
  pr(t);
  if (sizeof...(ts)) pw();
  pw(ts...);
}
template <class T, class... Ts>
void pc(const T& t, const Ts&... ts) {
  bool op = 0;
  if (parsepair(t)) op = 1;
  if (op) pr("{");
  pr(t);
  if (op) pr("}");
  if (sizeof...(ts)) pr(", ");
  pc(ts...);
}
namespace trace {
template <class T1, class T2>
void __f(const char* name, const T1& Xx, const T2& y) {
  pr("[", y, "] = ");
  ps(Xx);
}
template <class T1, class T2, class... Ts>
void __f(const char* name, const T1& Xx, const T2& y, const Ts&... rest) {
  const char* open = strchr(name, '[');
  pr("[", y, "]");
  __f(open + 1, Xx, rest...);
}
template <class T1, class T2, class... Ts>
void __f0(const char* name, const T1& Xx, const T2& y, const Ts&... rest) {
  const char* open = strchr(name, '[');
  pr(name, size_t(open - name));
  __f(name, Xx, y, rest...);
}
template <class T>
void __fn(int n, const char* name, const T& Xx) {
  for (int i = 0; i < n; i++) pr(name), __f(name, Xx[i], i);
}
}  // namespace trace
}  // namespace output
using namespace minmax;
using namespace input;
using namespace output;
using namespace output::trace;
const int N = 2e5 + 5;
vector<int> a, b;
vector<int> generate_pi(vector<int>& s) {
  int i, n = (int)(s).size();
  vector<int> pi(n);
  for (i = 1; i < n; i++) {
    int p = pi[i - 1];
    while (p and s[i] != s[p]) p = pi[p - 1];
    pi[i] = p + (s[i] == s[p]);
  }
  return pi;
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int i, n, m, ans = 0;
  re(n, m);
  a.resize(n);
  b.resize(m);
  re(a, b);
  vector<int> s;
  for (i = 1; i < m; i++) s.emplace_back(b[i] - b[i - 1]);
  s.emplace_back(INF);
  for (i = 1; i < n; i++) s.emplace_back(a[i] - a[i - 1]);
  auto pi = generate_pi(s);
  for (auto& x : pi)
    if (x == m - 1) ans++;
  ps(ans);
  return 0;
}

```