#include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
std::istream& operator>>(std::istream& i, pair<T, U>& p) {
  i >> p.first >> p.second;
  return i;
}
template <typename T>
std::istream& operator>>(std::istream& i, vector<T>& t) {
  for (auto& v : t) {
    i >> v;
  }
  return i;
}
template <typename T, typename U>
std::ostream& operator<<(std::ostream& o, const pair<T, U>& p) {
  o << p.first << ' ' << p.second;
  return o;
}
template <typename T>
std::ostream& operator<<(std::ostream& o, const vector<T>& t) {
  if (t.empty()) o << '\n';
  for (size_t i = 0; i < t.size(); ++i) {
    o << t[i] << " \n"[i == t.size() - 1];
  }
  return o;
}
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T, vector<T>, less<T>>;
unsigned int logceil(long long first) {
  return first ? 8 * sizeof(long long) - __builtin_clzll(first) : 0;
}
namespace std {
template <typename T, typename U>
struct hash<pair<T, U>> {
  hash<T> t;
  hash<U> u;
  size_t operator()(const pair<T, U>& p) const {
    return t(p.first) ^ (u(p.second) << 7);
  }
};
}  // namespace std
template <typename T, typename F>
T bsh(T l, T h, const F& f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      l = m + 1;
      r = m;
    } else {
      h = m - 1;
    }
  }
  return r;
}
template <typename F>
double bshd(double l, double h, const F& f, double p = 1e-9) {
  unsigned int r = 3 + (unsigned int)log2((h - l) / p);
  while (r--) {
    double m = (l + h) / 2;
    if (f(m)) {
      l = m;
    } else {
      h = m;
    }
  }
  return (l + h) / 2;
}
template <typename T, typename F>
T bsl(T l, T h, const F& f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      h = m - 1;
      r = m;
    } else {
      l = m + 1;
    }
  }
  return r;
}
template <typename F>
double bsld(double l, double h, const F& f, double p = 1e-9) {
  unsigned int r = 3 + (unsigned int)log2((h - l) / p);
  while (r--) {
    double m = (l + h) / 2;
    if (f(m)) {
      h = m;
    } else {
      l = m;
    }
  }
  return (l + h) / 2;
}
template <typename T>
T gcd(T a, T b) {
  if (a < b) swap(a, b);
  return b ? gcd(b, a % b) : a;
}
template <typename T>
class vector2 : public vector<vector<T>> {
 public:
  vector2() {}
  vector2(size_t a, size_t b, T t = T())
      : vector<vector<T>>(a, vector<T>(b, t)) {}
};
template <typename T>
class vector3 : public vector<vector2<T>> {
 public:
  vector3() {}
  vector3(size_t a, size_t b, size_t c, T t = T())
      : vector<vector2<T>>(a, vector2<T>(b, c, t)) {}
};
template <typename T>
class vector4 : public vector<vector3<T>> {
 public:
  vector4() {}
  vector4(size_t a, size_t b, size_t c, size_t d, T t = T())
      : vector<vector3<T>>(a, vector3<T>(b, c, d, t)) {}
};
template <typename T>
class vector5 : public vector<vector4<T>> {
 public:
  vector5() {}
  vector5(size_t a, size_t b, size_t c, size_t d, size_t e, T t = T())
      : vector<vector4<T>>(a, vector4<T>(b, c, d, e, t)) {}
};
template <typename T>
struct Fenwick {
  explicit Fenwick(unsigned int N = 0, T t = T())
      : N(1u << logceil(N)), F(this->N, t), t(t) {}
  explicit Fenwick(const vector<T>& A, T t = T())
      : N(1u << logceil(A.size())), F(A), t(t) {
    F.resize(N);
    fill(F.begin() + A.size(), F.end(), t);
    for (int i = 0; i < N; i++) {
      int j = i + lsb(i + 1);
      if (j < N) F[j] += F[i];
    }
  }
  void add(int i, T v) {
    while (i <= N) {
      F[i] += v;
      i += lsb(i + 1);
    }
  }
  T sum(int i) const {
    T sum(t);
    while (i) {
      sum += F[i - 1];
      i -= lsb(i);
    }
    return sum;
  }
  T range(int i, int j) const {
    j++;
    T s(t);
    while (j > i) {
      s += F[j - 1];
      j -= lsb(j);
    }
    while (i > j) {
      s -= F[i - 1];
      i -= lsb(i);
    }
    return s;
  }
  T get(int i) const { return range(i, i); }
  void set(int i, T v) { add(i, v - get(i)); }
  constexpr int lsb(int i) const { return i & -i; }
  unsigned int N;
  vector<T> F;
  T t;
  int max_lower(T v) {
    if (F[0] >= v) return -1;
    if (F[N - 1] < v) return N - 1;
    int first = 0;
    T a = t;
    for (int s = N >> 1; s > 0; s >>= 1)
      if (a + F[first + s - 1] < v) {
        a += F[first + s - 1];
        first += s;
      }
    return first;
  }
};
template <typename T>
struct Fenwick2 {
  explicit Fenwick2(unsigned int N = 0, T t = T())
      : N(1u << logceil(N)), F(this->N, this->N, t), t(t) {}
  void add(int first, int second, T v) {
    while (first <= N) {
      int z = second;
      while (z <= N) {
        F[first][z] += v;
        z += lsb(z + 1);
      }
      first += lsb(first + 1);
    }
  }
  T sum(int first, int second) {
    T sum(t);
    while (first <= N) {
      int z = second;
      while (z <= N) {
        sum += F[first][z];
        z -= lsb(z + 1);
      }
      first -= lsb(first + 1);
    }
    return sum;
  }
  T range(int x1, int y1, int x2, int y2) {
    T ans = sum(x2, y2);
    if (x1) ans -= sum(x1 - 1, y2);
    if (y1) ans -= sum(x2, y1 - 1);
    if (x1 && y1) ans += sum(x1 - 1, y1 - 1);
    return ans;
  }
  constexpr int lsb(int i) const { return i & -i; }
  unsigned int N;
  vector2<T> F;
  T t;
};
class E2MedianOnSegmentsGeneralCaseEdition {
 public:
  void solve(istream& cin, ostream& cout) {
    int N, M;
    cin >> N >> M;
    vector<int> A(N);
    cin >> A;
    auto solve = [&](vector<int> A, int M) {
      for (int& a : A) a = (a >= M) - (a < M);
      vector<int> B(N + 1, 0);
      for (int i = 0; i < N; ++i) {
        B[i + 1] = B[i] + (A[i] == 1) - (A[i] != 1);
      }
      long long ans = 0;
      Fenwick<int> F(2 * N + 1, 0);
      for (int l = 0; l < N; ++l) {
        F.add(B[l] + N, 1);
        ans += F.range(B[l + 1] + N, 2 * N);
      }
      return ans;
    };
    cout << solve(A, M + 1) - solve(A, M) << '\n';
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  E2MedianOnSegmentsGeneralCaseEdition solver;
  std::istream& in(std::cin);
  std::ostream& out(std::cout);
  solver.solve(in, out);
  return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

You are given a permutation p_1, p_2, ..., p_n. A permutation of length n is a sequence such that each integer between 1 and n occurs exactly once in the sequence.

Find the number of pairs of indices (l, r) (1 ≤ l ≤ r ≤ n) such that the value of the median of p_l, p_{l+1}, ..., p_r is exactly the given number m.

The median of a sequence is the value of the element which is in the middle of the sequence after sorting it in non-decreasing order. If the length of the sequence is even, the left of two middle elements is used.

For example, if a=[4, 2, 7, 5] then its median is 4 since after sorting the sequence, it will look like [2, 4, 5, 7] and the left of two middle elements is equal to 4. The median of [7, 1, 2, 9, 6] equals 6 since after sorting, the value 6 will be in the middle of the sequence.

Write a program to find the number of pairs of indices (l, r) (1 ≤ l ≤ r ≤ n) such that the value of the median of p_l, p_{l+1}, ..., p_r is exactly the given number m.

Input

The first line contains integers n and m (1 ≤ n ≤ 2⋅10^5, 1 ≤ m ≤ n) — the length of the given sequence and the required value of the median.

The second line contains a permutation p_1, p_2, ..., p_n (1 ≤ p_i ≤ n). Each integer between 1 and n occurs in p exactly once.

Output

Print the required number.

Examples

Input

5 4
2 4 5 3 1


Output

4


Input

5 5
1 2 3 4 5


Output

1


Input

15 8
1 15 2 14 3 13 4 8 12 5 11 6 10 7 9


Output

48

Note

In the first example, the suitable pairs of indices are: (1, 3), (2, 2), (2, 3) and (2, 4).

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
std::istream& operator>>(std::istream& i, pair<T, U>& p) {
  i >> p.first >> p.second;
  return i;
}
template <typename T>
std::istream& operator>>(std::istream& i, vector<T>& t) {
  for (auto& v : t) {
    i >> v;
  }
  return i;
}
template <typename T, typename U>
std::ostream& operator<<(std::ostream& o, const pair<T, U>& p) {
  o << p.first << ' ' << p.second;
  return o;
}
template <typename T>
std::ostream& operator<<(std::ostream& o, const vector<T>& t) {
  if (t.empty()) o << '\n';
  for (size_t i = 0; i < t.size(); ++i) {
    o << t[i] << " \n"[i == t.size() - 1];
  }
  return o;
}
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T, vector<T>, less<T>>;
unsigned int logceil(long long first) {
  return first ? 8 * sizeof(long long) - __builtin_clzll(first) : 0;
}
namespace std {
template <typename T, typename U>
struct hash<pair<T, U>> {
  hash<T> t;
  hash<U> u;
  size_t operator()(const pair<T, U>& p) const {
    return t(p.first) ^ (u(p.second) << 7);
  }
};
}  // namespace std
template <typename T, typename F>
T bsh(T l, T h, const F& f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      l = m + 1;
      r = m;
    } else {
      h = m - 1;
    }
  }
  return r;
}
template <typename F>
double bshd(double l, double h, const F& f, double p = 1e-9) {
  unsigned int r = 3 + (unsigned int)log2((h - l) / p);
  while (r--) {
    double m = (l + h) / 2;
    if (f(m)) {
      l = m;
    } else {
      h = m;
    }
  }
  return (l + h) / 2;
}
template <typename T, typename F>
T bsl(T l, T h, const F& f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      h = m - 1;
      r = m;
    } else {
      l = m + 1;
    }
  }
  return r;
}
template <typename F>
double bsld(double l, double h, const F& f, double p = 1e-9) {
  unsigned int r = 3 + (unsigned int)log2((h - l) / p);
  while (r--) {
    double m = (l + h) / 2;
    if (f(m)) {
      h = m;
    } else {
      l = m;
    }
  }
  return (l + h) / 2;
}
template <typename T>
T gcd(T a, T b) {
  if (a < b) swap(a, b);
  return b ? gcd(b, a % b) : a;
}
template <typename T>
class vector2 : public vector<vector<T>> {
 public:
  vector2() {}
  vector2(size_t a, size_t b, T t = T())
      : vector<vector<T>>(a, vector<T>(b, t)) {}
};
template <typename T>
class vector3 : public vector<vector2<T>> {
 public:
  vector3() {}
  vector3(size_t a, size_t b, size_t c, T t = T())
      : vector<vector2<T>>(a, vector2<T>(b, c, t)) {}
};
template <typename T>
class vector4 : public vector<vector3<T>> {
 public:
  vector4() {}
  vector4(size_t a, size_t b, size_t c, size_t d, T t = T())
      : vector<vector3<T>>(a, vector3<T>(b, c, d, t)) {}
};
template <typename T>
class vector5 : public vector<vector4<T>> {
 public:
  vector5() {}
  vector5(size_t a, size_t b, size_t c, size_t d, size_t e, T t = T())
      : vector<vector4<T>>(a, vector4<T>(b, c, d, e, t)) {}
};
template <typename T>
struct Fenwick {
  explicit Fenwick(unsigned int N = 0, T t = T())
      : N(1u << logceil(N)), F(this->N, t), t(t) {}
  explicit Fenwick(const vector<T>& A, T t = T())
      : N(1u << logceil(A.size())), F(A), t(t) {
    F.resize(N);
    fill(F.begin() + A.size(), F.end(), t);
    for (int i = 0; i < N; i++) {
      int j = i + lsb(i + 1);
      if (j < N) F[j] += F[i];
    }
  }
  void add(int i, T v) {
    while (i <= N) {
      F[i] += v;
      i += lsb(i + 1);
    }
  }
  T sum(int i) const {
    T sum(t);
    while (i) {
      sum += F[i - 1];
      i -= lsb(i);
    }
    return sum;
  }
  T range(int i, int j) const {
    j++;
    T s(t);
    while (j > i) {
      s += F[j - 1];
      j -= lsb(j);
    }
    while (i > j) {
      s -= F[i - 1];
      i -= lsb(i);
    }
    return s;
  }
  T get(int i) const { return range(i, i); }
  void set(int i, T v) { add(i, v - get(i)); }
  constexpr int lsb(int i) const { return i & -i; }
  unsigned int N;
  vector<T> F;
  T t;
  int max_lower(T v) {
    if (F[0] >= v) return -1;
    if (F[N - 1] < v) return N - 1;
    int first = 0;
    T a = t;
    for (int s = N >> 1; s > 0; s >>= 1)
      if (a + F[first + s - 1] < v) {
        a += F[first + s - 1];
        first += s;
      }
    return first;
  }
};
template <typename T>
struct Fenwick2 {
  explicit Fenwick2(unsigned int N = 0, T t = T())
      : N(1u << logceil(N)), F(this->N, this->N, t), t(t) {}
  void add(int first, int second, T v) {
    while (first <= N) {
      int z = second;
      while (z <= N) {
        F[first][z] += v;
        z += lsb(z + 1);
      }
      first += lsb(first + 1);
    }
  }
  T sum(int first, int second) {
    T sum(t);
    while (first <= N) {
      int z = second;
      while (z <= N) {
        sum += F[first][z];
        z -= lsb(z + 1);
      }
      first -= lsb(first + 1);
    }
    return sum;
  }
  T range(int x1, int y1, int x2, int y2) {
    T ans = sum(x2, y2);
    if (x1) ans -= sum(x1 - 1, y2);
    if (y1) ans -= sum(x2, y1 - 1);
    if (x1 && y1) ans += sum(x1 - 1, y1 - 1);
    return ans;
  }
  constexpr int lsb(int i) const { return i & -i; }
  unsigned int N;
  vector2<T> F;
  T t;
};
class E2MedianOnSegmentsGeneralCaseEdition {
 public:
  void solve(istream& cin, ostream& cout) {
    int N, M;
    cin >> N >> M;
    vector<int> A(N);
    cin >> A;
    auto solve = [&](vector<int> A, int M) {
      for (int& a : A) a = (a >= M) - (a < M);
      vector<int> B(N + 1, 0);
      for (int i = 0; i < N; ++i) {
        B[i + 1] = B[i] + (A[i] == 1) - (A[i] != 1);
      }
      long long ans = 0;
      Fenwick<int> F(2 * N + 1, 0);
      for (int l = 0; l < N; ++l) {
        F.add(B[l] + N, 1);
        ans += F.range(B[l + 1] + N, 2 * N);
      }
      return ans;
    };
    cout << solve(A, M + 1) - solve(A, M) << '\n';
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  E2MedianOnSegmentsGeneralCaseEdition solver;
  std::istream& in(std::cin);
  std::ostream& out(std::cout);
  solver.solve(in, out);
  return 0;
}

```