You are given an array a of length 2^n. You should process q queries on it. Each query has one of the following 4 types: 

  1. Replace(x, k) — change a_x to k; 
  2. Reverse(k) — reverse each subarray [(i-1) ⋅ 2^k+1, i ⋅ 2^k] for all i (i ≥ 1); 
  3. Swap(k) — swap subarrays [(2i-2) ⋅ 2^k+1, (2i-1) ⋅ 2^k] and [(2i-1) ⋅ 2^k+1, 2i ⋅ 2^k] for all i (i ≥ 1); 
  4. Sum(l, r) — print the sum of the elements of subarray [l, r]. 



Write a program that can quickly process given queries.

Input

The first line contains two integers n, q (0 ≤ n ≤ 18; 1 ≤ q ≤ 10^5) — the length of array a and the number of queries.

The second line contains 2^n integers a_1, a_2, …, a_{2^n} (0 ≤ a_i ≤ 10^9).

Next q lines contains queries — one per line. Each query has one of 4 types: 

  * "1 x k" (1 ≤ x ≤ 2^n; 0 ≤ k ≤ 10^9) — Replace(x, k); 
  * "2 k" (0 ≤ k ≤ n) — Reverse(k); 
  * "3 k" (0 ≤ k < n) — Swap(k); 
  * "4 l r" (1 ≤ l ≤ r ≤ 2^n) — Sum(l, r). 



It is guaranteed that there is at least one Sum query.

Output

Print the answer for each Sum query.

Examples

Input


2 3
7 4 9 9
1 2 8
3 1
4 2 4


Output


24


Input


3 8
7 0 8 8 7 1 5 2
4 3 7
2 1
3 2
4 1 6
2 3
1 5 16
4 8 8
3 0


Output


29
22
1

Note

In the first sample, initially, the array a is equal to \{7,4,9,9\}.

After processing the first query. the array a becomes \{7,8,9,9\}.

After processing the second query, the array a_i becomes \{9,9,7,8\}

Therefore, the answer to the third query is 9+7+8=24.

In the second sample, initially, the array a is equal to \{7,0,8,8,7,1,5,2\}. What happens next is: 

  1. Sum(3, 7) → 8 + 8 + 7 + 1 + 5 = 29; 
  2. Reverse(1) → \{0,7,8,8,1,7,2,5\}; 
  3. Swap(2) → \{1,7,2,5,0,7,8,8\}; 
  4. Sum(1, 6) → 1 + 7 + 2 + 5 + 0 + 7 = 22; 
  5. Reverse(3) → \{8,8,7,0,5,2,7,1\}; 
  6. Replace(5, 16) → \{8,8,7,0,16,2,7,1\}; 
  7. Sum(8, 8) → 1; 
  8. Swap(0) → \{8,8,0,7,2,16,1,7\}. 
#include <bits/stdc++.h>
using namespace std;
using ll = int64_t;
using ull = uint64_t;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using f64 = double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using ld = long double;
namespace io {
const int BUFSIZE = 1 << 20;
int isize, osize;
char ibuf[BUFSIZE + 10], obuf[BUFSIZE + 10];
char *is, *it, *os = obuf, *ot = obuf + BUFSIZE;
char getchar() {
  if (is == it) {
    is = ibuf;
    it = ibuf + fread(ibuf, 1, BUFSIZE, stdin);
    if (is == it) return EOF;
  }
  return *is++;
}
char getalpha() {
  char c = getchar();
  while (!isalpha(c)) c = getchar();
  return c;
}
void putchar(char c) {
  *os++ = c;
  if (os == ot) {
    fwrite(obuf, 1, BUFSIZE, stdout);
    os = obuf;
  }
}
int inp() {
  int x = 0, f = 0;
  char ch;
  for (ch = getchar(); !isdigit(ch); ch = getchar()) {
    if (ch == EOF) return -1;
    if (ch == '-') f = 1;
  }
  for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar())
    ;
  return f ? -x : x;
}
ll inp_ll() {
  ll x = 0;
  int f = 0;
  char ch;
  for (ch = getchar(); !isdigit(ch); ch = getchar())
    if (ch == '-') f = 1;
  for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar())
    ;
  return f ? -x : x;
}
template <class T>
bool read(T& x) {
  x = 0;
  int f = 0;
  char ch;
  for (ch = getchar(); !isdigit(ch); ch = getchar()) {
    if (ch == EOF) return 0;
    if (ch == '-') f = 1;
  }
  for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar())
    ;
  if (f) x = -x;
  return 1;
}
bool read(char* s) {
  char* t = s;
  char ch = getchar();
  for (; ch == ' ' || ch == '\n'; ch = getchar())
    ;
  for (; ch != ' ' && ch != '\n' && ch != EOF; ch = getchar()) *t++ = ch;
  *t = 0;
  return s != t;
}
template <class T, class... Args>
bool read(T& x, Args&... args) {
  return read(x) && read(args...);
}
template <class T>
bool readln(T& x) {
  x = 0;
  int f = 0;
  char ch;
  for (ch = getchar(); !isdigit(ch); ch = getchar()) {
    if (ch == EOF) return 0;
    if (ch == '-') f = 1;
  }
  for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar())
    ;
  if (f) x = -x;
  for (; ch != '\n' && ch != EOF; ch = getchar())
    ;
  return 1;
}
bool readln(char* s) {
  char* t = s;
  while (1) {
    char ch = getchar();
    if (ch == '\n' || ch == EOF) break;
    *t++ = ch;
  }
  *t = 0;
  return s != t;
}
template <class T, class... Args>
bool readln(T& x, Args&... args) {
  return read(x) && readln(args...);
}
template <class T>
void write(T x) {
  static char s[22];
  static char* it = s + 20;
  static char* end = s + 20;
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  do {
    *--it = x % 10 + '0';
    x /= 10;
  } while (x);
  for (; it < end; ++it) putchar(*it);
}
void write(const char* s) {
  for (; *s; ++s) putchar(*s);
}
template <>
void write(char* s) {
  write((const char*)s);
}
template <>
void write(char c) {
  putchar(c);
}
template <class T, class... Args>
void write(T x, Args... args) {
  write(x);
  write(args...);
}
void writeln() { putchar('\n'); }
template <class T, class... Args>
void writeln(T x, Args... args) {
  write(x);
  writeln(args...);
}
template <class Iterator>
bool input(Iterator st, Iterator ed) {
  for (; st != ed; ++st) {
    if (!read(*st)) return false;
  }
  return true;
}
template <class T>
bool input(T& a) {
  return input(a.begin(), a.end());
}
template <class Iterator>
void print(Iterator st, Iterator ed, const char* c = " ") {
  int flag = 0;
  for (; st != ed; ++st) {
    if (flag) write(c);
    flag = 1;
    write(*st);
  }
  writeln();
}
template <class T>
void print(const T& a, const char* c = " ") {
  print(a.begin(), a.end(), c);
}
struct ender {
  ~ender() {
    if (os != obuf) fwrite(obuf, 1, os - obuf, stdout);
  }
} __ender;
}  // namespace io
int64_t power(int64_t a, int64_t b, int64_t p) {
  if (!b) return 1;
  int64_t t = power(a, b >> 1, p);
  t = t * t % p;
  if (b & 1) t = t * a % p;
  return t;
}
pll exgcd(ll a, ll b) {
  if (b == 0) return {1, 0};
  auto e = exgcd(b, a % b);
  ll x = e.first;
  ll y = e.second;
  return {y, x - a / b * y};
}
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
using namespace io;
template <class T>
inline void freshmin(T& a, const T& b) {
  if (a > b) a = b;
}
template <class T>
inline void freshmax(T& a, const T& b) {
  if (a < b) a = b;
}
int dx[] = {-1, 1, 0, 0, -1, -1, 1, 1};
int dy[] = {0, 0, -1, 1, -1, 1, -1, 1};
template <class T>
T det(T x1, T y1, T x2, T y2, T x3, T y3) {
  return x1 * y2 - x2 * y1 + x2 * y3 - x3 * y2 + x3 * y1 - x1 * y3;
}
void init() {}
const int MAXN = 1000010;
void solve() {
  int n, q;
  read(n, q);
  int N = 1 << n;
  vector<ll> a(N);
  input(a);
  if (n == 0) {
    while (q--) {
      int op;
      read(op);
      if (op == 1) {
        int x, p;
        read(x, p);
        x -= 1;
        a[x] = p;
      } else if (op == 2) {
        int k;
        read(k);
      } else if (op == 3) {
        int k;
        read(k);
      } else {
        assert(op == 4);
        int x, y;
        read(x, y);
        x -= 1;
        y -= 1;
        ll res = a[0];
        writeln(res);
      }
    }
    return;
  }
  vector<vector<ll>> s(N, vector<ll>(n));
  auto add = [&](int x, ll p) {
    for (int k = n - 1; k >= 0; --k) {
      s[x >> k << k][k] += p;
    }
  };
  for (int i = 0; i < N; ++i) {
    add(i, a[i]);
  }
  vector<int> r(n);
  auto calc = [&](int x) {
    if (x == N) {
      return s[1 << (n - 1)][n - 1] + s[0][n - 1];
    }
    ll res = 0;
    int prefix = 0;
    for (int k = n - 1; k >= 0; --k) {
      if (x >> k & 1) {
        res += s[prefix | r[k] << k][k];
      }
      prefix |= (r[k] ^ (x >> k & 1)) << k;
    }
    return res;
  };
  while (q--) {
    int op;
    read(op);
    if (op == 1) {
      int x, p;
      read(x, p);
      x -= 1;
      for (int k = n - 1; k >= 0; --k) {
        if (r[k]) x ^= 1 << k;
      }
      add(x, p - a[x]);
      a[x] = p;
    } else if (op == 2) {
      int k;
      read(k);
      for (int i = 0; i < k; ++i) r[i] ^= 1;
    } else if (op == 3) {
      int k;
      read(k);
      r[k] ^= 1;
    } else {
      assert(op == 4);
      int x, y;
      read(x, y);
      x -= 1;
      y -= 1;
      ll res = calc(y + 1) - calc(x);
      writeln(res);
    }
  }
}
int main() {
  int T = 1;
  init();
  for (int test = 1; test <= T; ++test) {
    solve();
  }
  return 0;
}
