Problem: One day two students, Grisha and Diana, found themselves in the university chemistry lab. In the lab the students found n test tubes with mercury numbered from 1 to n and decided to conduct an experiment.

The experiment consists of q steps. On each step, one of the following actions occurs:

  1. Diana pours all the contents from tube number pi and then pours there exactly xi liters of mercury. 
  2. Let's consider all the ways to add vi liters of water into the tubes; for each way let's count the volume of liquid (water and mercury) in the tube with water with maximum amount of liquid; finally let's find the minimum among counted maximums. That is the number the students want to count. At that, the students don't actually pour the mercury. They perform calculations without changing the contents of the tubes. 



Unfortunately, the calculations proved to be too complex and the students asked you to help them. Help them conduct the described experiment.

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 105) — the number of tubes ans the number of experiment steps. The next line contains n space-separated integers: h1, h2, ..., hn (0 ≤ hi ≤ 109), where hi is the volume of mercury in the і-th tube at the beginning of the experiment.

The next q lines contain the game actions in the following format:

  * A line of form "1 pi xi" means an action of the first type (1 ≤ pi ≤ n; 0 ≤ xi ≤ 109). 
  * A line of form "2 vi" means an action of the second type (1 ≤ vi ≤ 1015). 



It is guaranteed that there is at least one action of the second type. It is guaranteed that all numbers that describe the experiment are integers.

Output

For each action of the second type print the calculated value. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.

Examples

Input

3 3
1 2 0
2 2
1 2 1
2 3


Output

1.50000
1.66667


Input

4 5
1 3 0 1
2 3
2 1
1 3 2
2 3
2 4


Output

1.66667
1.00000
2.33333
2.66667

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
namespace IO {
int double_len(6);
bool spacebar_can_see(1);
const char NUMBER_TO_CHAR[36] = {
    48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 65, 66, 67, 68, 69, 70, 71, 72,
    73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90};
const int CHAR_TO_NUMBER[128] = {
    0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
    0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
    0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  2,  3,  4,  5,  6,  7,  8,
    9,  0,  0,  0,  0,  0,  0,  0,  10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
    21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 0,  0,  0,  0,
    0,  0,  10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26,
    27, 28, 29, 30, 31, 32, 33, 34, 35, 0,  0,  0,  0,  0};
template <typename T>
class Number {
 public:
  unsigned int len;
  int hex;
  T number;
  inline Number(const T number = 0, const int hex = 10, const int len = 0)
      : number(number), hex(hex), len(len) {}
  inline operator T() const { return number; }
  inline Number<T> &operator=(const T &a) {
    number = a;
    return *this;
  }
};
inline bool CanSee(const char ch) {
  return spacebar_can_see ? (31 < ch && ch < 127) : (32 < ch && ch < 127);
}
inline bool IsNumber(const char ch) { return (47 < ch && ch < 58); }
inline bool IsNumber_(const int hex, const char ch) {
  return (47 < ch && ch < 48 + hex) || (64 < ch && ch < 55 + hex) ||
         (96 < ch && ch < 87 + hex);
}
const int IN_BUF = 1 << 23, OUT_BUF = 1 << 23;
char buf[IN_BUF], *ps = buf, *pt = buf, pbuf[OUT_BUF], *pp = pbuf;
inline char GetChar() {
  if (ps == pt) {
    ps = buf;
    pt = buf + fread(buf, 1, IN_BUF, stdin);
  }
  return ps == pt ? EOF : *ps++;
}
inline void PutChar(const char ch) {
  if (pp == pbuf + OUT_BUF) {
    fwrite(pbuf, 1, OUT_BUF, stdout);
    pp = pbuf;
  }
  *pp++ = ch;
}
char read_ch(10);
template <class T>
inline T ReadInt() {
  register T x(0);
  register bool f(1);
  while (!IsNumber(read_ch) && (~read_ch)) {
    if (read_ch == 45) {
      f = 0;
    }
    read_ch = GetChar();
  }
  while (IsNumber(read_ch) && (~read_ch)) {
    x = (x << 1) + (x << 3) + (read_ch ^ 48);
    read_ch = GetChar();
  }
  return f ? x : -x;
}
template <class T>
inline T ReadUInt() {
  register T x(0);
  while (!IsNumber(read_ch) && (~read_ch)) {
    read_ch = GetChar();
  }
  while (IsNumber(read_ch) && (~read_ch)) {
    x = (x << 1) + (x << 3) + (read_ch ^ 48);
    read_ch = GetChar();
  }
  return x;
}
template <class T>
inline T ReadKInt(const int hex) {
  register T x(0);
  register bool f(1);
  while (!IsNumber_(hex, read_ch) && (~read_ch)) {
    if (read_ch == 45) {
      f = 0;
    }
    read_ch = GetChar();
  }
  while (IsNumber_(hex, read_ch) && (~read_ch)) {
    x = x * hex + CHAR_TO_NUMBER[read_ch];
    read_ch = GetChar();
  }
  return f ? x : -x;
}
template <class T>
inline T ReadUKInt(const int hex) {
  register T x(0);
  while (!IsNumber_(hex, read_ch) && (~read_ch)) {
    read_ch = GetChar();
  }
  while (IsNumber_(hex, read_ch) && (~read_ch)) {
    x = x * hex + CHAR_TO_NUMBER[read_ch];
    read_ch = GetChar();
  }
  return x;
}
inline double ReadDouble() {
  register long long int_num(ReadInt<long long>());
  if (read_ch == 46) {
    register double pow10(1.0), result(0);
    read_ch = GetChar();
    while (IsNumber(read_ch) && (~read_ch)) {
      pow10 /= 10.0;
      result += pow10 * (read_ch ^ 48);
      read_ch = GetChar();
    }
    return int_num + (int_num < 0 ? -result : result);
  } else {
    return (double)int_num;
  }
}
inline void ReadT(int &x) { x = ReadInt<int>(); }
inline void ReadT(long long &x) { x = ReadInt<long long>(); }
inline void ReadT(bool &x) { x = ReadUInt<bool>(); }
inline void ReadT(unsigned int &x) { x = ReadUInt<unsigned int>(); }
inline void ReadT(unsigned long long &x) { x = ReadUInt<unsigned long long>(); }
inline void ReadT(double &x) { x = ReadDouble(); }
inline void ReadT(char &ch) {
  for (; !CanSee(read_ch) && (~read_ch); read_ch = GetChar())
    ;
  ch = read_ch;
  read_ch = 10;
}
inline void ReadT(Number<int> &x) { x.number = ReadKInt<int>(x.hex); }
inline void ReadT(Number<long long> &x) {
  x.number = ReadKInt<long long>(x.hex);
}
inline void ReadT(Number<unsigned int> &x) {
  x.number = ReadUKInt<unsigned int>(x.hex);
}
inline void ReadT(Number<unsigned long long> &x) {
  x.number = ReadUKInt<unsigned long long>(x.hex);
}
inline void ReadT(char *s) {
  register int len(0);
  for (; !CanSee(read_ch) && (~read_ch); read_ch = GetChar())
    ;
  for (; CanSee(read_ch) && (~read_ch); read_ch = GetChar()) {
    s[len++] = read_ch;
  }
  s[len] = 0;
  read_ch = 10;
}
template <class T>
inline void Read(T &t) {
  ReadT(t);
}
template <class T, class... Args>
void Read(T &t, Args &...args) {
  ReadT(t);
  Read(args...);
}
template <class T>
inline void WriteUInt(T x) {
  static char out_number[25];
  static int cnt;
  out_number[cnt = 1] = x % 10 ^ 48;
  while (x /= 10) {
    out_number[++cnt] = x % 10 ^ 48;
  }
  while (cnt) {
    PutChar(out_number[cnt--]);
  }
}
template <class T>
inline void WriteInt(const T x) {
  if (x < 0) {
    PutChar(45);
    WriteUInt(-x);
    return;
  }
  WriteUInt(x);
}
template <class T>
inline void WriteUKInt(T x, const int hex, int len) {
  static char out_number[25];
  static int cnt;
  out_number[cnt = 1] = NUMBER_TO_CHAR[x % hex];
  while (x /= hex) {
    out_number[++cnt] = NUMBER_TO_CHAR[x % hex];
  }
  len -= cnt;
  while (0 < len--) {
    PutChar(48);
  }
  while (cnt) {
    PutChar(out_number[cnt--]);
  }
}
template <class T>
inline void WriteKInt(const T x, const int hex, const int len) {
  if (x < 0) {
    PutChar(45);
    WriteUKInt(-x, hex, len - 1);
    return;
  }
  WriteUKInt(x, hex, len);
}
inline void WriteDouble(double x, int len) {
  if (x < 0) {
    PutChar(45);
    x = -x;
  }
  WriteUInt<unsigned long long>((unsigned long long)x);
  if (len) {
    x -= (int)x;
    PutChar(46);
    while (len--) {
      x *= 10;
      if (!(unsigned long long)x) {
        PutChar(48);
      }
    }
    if ((unsigned long long)x) {
      WriteUInt<unsigned long long>((unsigned long long)x);
    }
  }
}
inline void WriteT(const int x) { WriteInt<int>(x); }
inline void WriteT(const long long x) { WriteInt<long long>(x); }
inline void WriteT(const bool x) { PutChar(x | 48); }
inline void WriteT(const unsigned int x) { WriteUInt<unsigned int>(x); }
inline void WriteT(const unsigned long long x) {
  WriteUInt<unsigned long long>(x);
}
inline void WriteT(const double x) { WriteDouble(x, double_len); }
inline void WriteT(const char *s) {
  while (*s) {
    PutChar(*s++);
  }
}
inline void WriteT(const char x) { PutChar(x); }
inline void WriteT(const Number<int> x) { WriteKInt(x.number, x.hex, x.len); }
inline void WriteT(const Number<long long> x) {
  WriteKInt(x.number, x.hex, x.len);
}
inline void WriteT(const Number<unsigned int> x) {
  WriteUKInt(x.number, x.hex, x.len);
}
inline void WriteT(const Number<unsigned long long> x) {
  WriteUKInt(x.number, x.hex, x.len);
}
template <class T>
inline void Write(const T t) {
  WriteT(t);
}
template <class T, class... Args>
void Write(const T t, const Args... args) {
  WriteT(t);
  Write(args...);
}
inline void Writeln() { PutChar(10); }
template <class T>
inline void Writeln(const T t) {
  WriteT(t);
  PutChar(10);
}
template <class... Args>
inline void Writeln(const Args... args) {
  Write(args...);
  PutChar(10);
}
template <class... Args>
inline void WriteExit(const Args... args) {
  Write(args...);
  PutChar(10);
  exit(0);
}
template <class... Args>
inline void DeBug(const Args... args) {}
template <class... Args>
inline void DeBugln(const Args... args) {}
inline void DeBugln() {}
class CodeToDo {
 public:
  inline CodeToDo() { srand(time(0)); }
  inline ~CodeToDo() {
    double_len = 3;
    DeBugln("\nTime=", (double)clock() / CLOCKS_PER_SEC, "s");
    fwrite(pbuf, 1, pp - pbuf, stdout);
  }
} code_to_do;
}  // namespace IO
using namespace IO;
using namespace std;
template <typename T>
inline T Max(const T a, const T b) {
  return a < b ? b : a;
}
template <typename T, typename... Args>
T Max(const T a, const Args... args) {
  return Max(a, Max(args...));
}
template <typename T>
inline T Min(const T a, const T b) {
  return a < b ? a : b;
}
template <typename T, typename... Args>
T Min(const T a, const Args... args) {
  return Min(a, Min(args...));
}
template <typename T>
inline void Swap(T &a, T &b) {
  register T temp = a;
  a = b;
  b = temp;
}
const int MAXN = 1e5 + 5;
int n, m;
int arr[MAXN];
int root = 0;
namespace SGT {
class SegmentTree {
 public:
  int lson, rson;
  int sum;
  long long sum_;
} sgt[MAXN * 32];
int sgt_cnt = 0;
inline void PushUp(const int now) {
  sgt[now].sum = sgt[sgt[now].lson].sum + sgt[sgt[now].rson].sum;
  sgt[now].sum_ = sgt[sgt[now].lson].sum_ + sgt[sgt[now].rson].sum_;
}
void Updata(const int val, const int add, int &now, const int left = 0,
            const int right = 1000000000) {
  if (val < left || right < val) {
    return;
  }
  if (!now) {
    now = ++sgt_cnt;
  }
  if (left == right) {
    sgt[now].sum += add;
    sgt[now].sum_ += add * val;
    return;
  }
  Updata(val, add, sgt[now].lson, left, ((left + right) >> 1));
  Updata(val, add, sgt[now].rson, ((left + right) >> 1) + 1, right);
  PushUp(now);
}
double Query(const long long val, const int now, const int left = 0,
             const int right = 1000000000, const long long sum = 0,
             const long long sum_ = 0) {
  if (left == right) {
    return (val + sgt[now].sum_ + sum_) * 1.0 / (sgt[now].sum + sum);
  }
  if (sum_ + sgt[sgt[now].lson].sum_ + val <
      1ll * (sum + sgt[sgt[now].lson].sum) * (((left + right) >> 1) + 1)) {
    return Query(val, sgt[now].lson, left, ((left + right) >> 1), sum, sum_);
  }
  return Query(val, sgt[now].rson, ((left + right) >> 1) + 1, right,
               sum + sgt[sgt[now].lson].sum, sum_ + sgt[sgt[now].lson].sum_);
}
}  // namespace SGT
int main() {
  Read(n, m);
  for (register int i = (1); i <= (n); ++i) {
    Read(arr[i]);
    SGT::Updata(arr[i], 1, root);
  }
  int opt, p, x;
  long long ml;
  for (register int i = (1); i <= (m); ++i) {
    Read(opt);
    if (opt == 1) {
      Read(p, x);
      SGT::Updata(arr[p], -1, root);
      arr[p] = x;
      SGT::Updata(arr[p], 1, root);
    }
    if (opt == 2) {
      Read(ml);
      Writeln(SGT::Query(ml, root));
    }
  }
  return 0;
}