#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:16777216")
int allocator_pos = 0;
char allocator_memory[(int)2e8];
inline void *operator new(size_t n) {
  char *res = allocator_memory + allocator_pos;
  allocator_pos += n;
  return (void *)res;
}
inline void operator delete(void *) noexcept {}
template <class T = long long>
inline T readInt();
inline double readDouble();
inline long long readUInt();
inline int readChar();
inline void readWord(char *s);
inline bool readLine(char *s);
inline bool isEof();
inline int getChar();
inline int peekChar();
inline bool seekEof();
inline void skipBlanks();
template <class T>
inline void writeInt(T x, char end = 0, int len = -1);
inline void writeChar(int x);
inline void writeWord(const char *s);
inline void writeDouble(double x, int len = 0);
inline void flush();
static struct buffer_flusher_t {
  ~buffer_flusher_t() { flush(); }
} buffer_flusher;
static const int buf_size = 4096;
static unsigned char buf[buf_size];
static int buf_len = 0, buf_pos = 0;
inline bool isEof() {
  if (buf_pos == buf_len) {
    buf_pos = 0, buf_len = fread(buf, 1, buf_size, stdin);
    if (buf_pos == buf_len) return 1;
  }
  return 0;
}
inline int getChar() { return isEof() ? -1 : buf[buf_pos++]; }
inline int peekChar() { return isEof() ? -1 : buf[buf_pos]; }
inline bool seekEof() {
  int c;
  while ((c = peekChar()) != -1 && c <= 32) buf_pos++;
  return c == -1;
}
inline void skipBlanks() {
  while (!isEof() && buf[buf_pos] <= 32U) buf_pos++;
}
inline int readChar() {
  int c = getChar();
  while (c != -1 && c <= 32) c = getChar();
  return c;
}
inline long long readUInt() {
  int c = readChar(), x = 0;
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return x;
}
template <class T>
inline T readInt() {
  int s = 1, c = readChar();
  T x = 0;
  if (c == '-')
    s = -1, c = getChar();
  else if (c == '+')
    c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return s == 1 ? x : -x;
}
inline double readDouble() {
  int s = 1, c = readChar();
  double x = 0;
  if (c == '-') s = -1, c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  if (c == '.') {
    c = getChar();
    double coef = 1;
    while ('0' <= c && c <= '9') x += (c - '0') * (coef *= 1e-1), c = getChar();
  }
  return s == 1 ? x : -x;
}
inline void readWord(char *s) {
  int c = readChar();
  while (c > 32) *s++ = c, c = getChar();
  *s = 0;
}
inline bool readLine(char *s) {
  int c = getChar();
  while (c != '\n' && c != -1) *s++ = c, c = getChar();
  *s = 0;
  return c != -1;
}
static int write_buf_pos = 0;
static char write_buf[buf_size];
inline void writeChar(int x) {
  if (write_buf_pos == buf_size)
    fwrite(write_buf, 1, buf_size, stdout), write_buf_pos = 0;
  write_buf[write_buf_pos++] = x;
}
inline void flush() {
  if (write_buf_pos)
    fwrite(write_buf, 1, write_buf_pos, stdout), write_buf_pos = 0;
}
template <class T>
inline void writeInt(T x, char end, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  char s[24];
  int n = 0;
  while (x || !n) s[n++] = '0' + x % 10, x /= 10;
  while (n < output_len) s[n++] = '0';
  while (n--) writeChar(s[n]);
  if (end) writeChar(end);
}
inline void writeWord(const char *s) {
  while (*s) writeChar(*s++);
}
inline void writeDouble(double x, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  int t = (int)x;
  writeInt(t), x -= t;
  writeChar('.');
  for (int i = output_len - 1; i > 0; i--) {
    x *= 10;
    t = std::min(9, (int)x);
    writeChar('0' + t), x -= t;
  }
  x *= 10;
  t = std::min(9, (int)(x + 0.5));
  writeChar('0' + t);
}
using namespace std;
struct Point {
  int x;
  int y;
};
int main() {
  int n = readInt();
  int m = readInt();
  vector<int> a(n);
  int u = 0;
  for (int i = 0; i < n; i++) {
    a[i] = readInt();
    if (a[i] == m) u = i;
  }
  unordered_map<int, int> dif;
  dif[0]++;
  int now = 0;
  for (int i = u + 1; i < n; i++) {
    if (a[i] > m)
      now++;
    else
      now--;
    dif[now]++;
  }
  long long ans = 0;
  now = 0;
  for (int i = u - 1; i >= 0; i--) {
    if (a[i] > m)
      now++;
    else
      now--;
    ans += dif[-now];
    ans += dif[1 - now];
  }
  writeInt(ans + dif[0] + dif[1]);
  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>
#pragma comment(linker, "/STACK:16777216")
int allocator_pos = 0;
char allocator_memory[(int)2e8];
inline void *operator new(size_t n) {
  char *res = allocator_memory + allocator_pos;
  allocator_pos += n;
  return (void *)res;
}
inline void operator delete(void *) noexcept {}
template <class T = long long>
inline T readInt();
inline double readDouble();
inline long long readUInt();
inline int readChar();
inline void readWord(char *s);
inline bool readLine(char *s);
inline bool isEof();
inline int getChar();
inline int peekChar();
inline bool seekEof();
inline void skipBlanks();
template <class T>
inline void writeInt(T x, char end = 0, int len = -1);
inline void writeChar(int x);
inline void writeWord(const char *s);
inline void writeDouble(double x, int len = 0);
inline void flush();
static struct buffer_flusher_t {
  ~buffer_flusher_t() { flush(); }
} buffer_flusher;
static const int buf_size = 4096;
static unsigned char buf[buf_size];
static int buf_len = 0, buf_pos = 0;
inline bool isEof() {
  if (buf_pos == buf_len) {
    buf_pos = 0, buf_len = fread(buf, 1, buf_size, stdin);
    if (buf_pos == buf_len) return 1;
  }
  return 0;
}
inline int getChar() { return isEof() ? -1 : buf[buf_pos++]; }
inline int peekChar() { return isEof() ? -1 : buf[buf_pos]; }
inline bool seekEof() {
  int c;
  while ((c = peekChar()) != -1 && c <= 32) buf_pos++;
  return c == -1;
}
inline void skipBlanks() {
  while (!isEof() && buf[buf_pos] <= 32U) buf_pos++;
}
inline int readChar() {
  int c = getChar();
  while (c != -1 && c <= 32) c = getChar();
  return c;
}
inline long long readUInt() {
  int c = readChar(), x = 0;
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return x;
}
template <class T>
inline T readInt() {
  int s = 1, c = readChar();
  T x = 0;
  if (c == '-')
    s = -1, c = getChar();
  else if (c == '+')
    c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return s == 1 ? x : -x;
}
inline double readDouble() {
  int s = 1, c = readChar();
  double x = 0;
  if (c == '-') s = -1, c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  if (c == '.') {
    c = getChar();
    double coef = 1;
    while ('0' <= c && c <= '9') x += (c - '0') * (coef *= 1e-1), c = getChar();
  }
  return s == 1 ? x : -x;
}
inline void readWord(char *s) {
  int c = readChar();
  while (c > 32) *s++ = c, c = getChar();
  *s = 0;
}
inline bool readLine(char *s) {
  int c = getChar();
  while (c != '\n' && c != -1) *s++ = c, c = getChar();
  *s = 0;
  return c != -1;
}
static int write_buf_pos = 0;
static char write_buf[buf_size];
inline void writeChar(int x) {
  if (write_buf_pos == buf_size)
    fwrite(write_buf, 1, buf_size, stdout), write_buf_pos = 0;
  write_buf[write_buf_pos++] = x;
}
inline void flush() {
  if (write_buf_pos)
    fwrite(write_buf, 1, write_buf_pos, stdout), write_buf_pos = 0;
}
template <class T>
inline void writeInt(T x, char end, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  char s[24];
  int n = 0;
  while (x || !n) s[n++] = '0' + x % 10, x /= 10;
  while (n < output_len) s[n++] = '0';
  while (n--) writeChar(s[n]);
  if (end) writeChar(end);
}
inline void writeWord(const char *s) {
  while (*s) writeChar(*s++);
}
inline void writeDouble(double x, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  int t = (int)x;
  writeInt(t), x -= t;
  writeChar('.');
  for (int i = output_len - 1; i > 0; i--) {
    x *= 10;
    t = std::min(9, (int)x);
    writeChar('0' + t), x -= t;
  }
  x *= 10;
  t = std::min(9, (int)(x + 0.5));
  writeChar('0' + t);
}
using namespace std;
struct Point {
  int x;
  int y;
};
int main() {
  int n = readInt();
  int m = readInt();
  vector<int> a(n);
  int u = 0;
  for (int i = 0; i < n; i++) {
    a[i] = readInt();
    if (a[i] == m) u = i;
  }
  unordered_map<int, int> dif;
  dif[0]++;
  int now = 0;
  for (int i = u + 1; i < n; i++) {
    if (a[i] > m)
      now++;
    else
      now--;
    dif[now]++;
  }
  long long ans = 0;
  now = 0;
  for (int i = u - 1; i >= 0; i--) {
    if (a[i] > m)
      now++;
    else
      now--;
    ans += dif[-now];
    ans += dif[1 - now];
  }
  writeInt(ans + dif[0] + dif[1]);
  return 0;
}

```