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 = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <typename T>
using vec = vector<T>;
template <typename T>
using Prior = priority_queue<T>;
template <typename T>
using prior = priority_queue<T, vec<T>, greater<T>>;
const int INF = 1e9 + 1;
const ll LLINF = (ll)4 * 1e18;
const ll MOD = 1e9 + 7;
const double PI = 3.14159265358;
const double EPS = 1e-8;
const int xx[8] = {0, 1, 0, -1, 1, 1, -1, -1};
const int yy[8] = {1, 0, -1, 0, 1, -1, -1, 1};
template <typename T>
void dbg(T x) {
  cerr << x << '\n';
}
template <typename T, typename... A>
void dbg(T x, A... y) {
  cerr << x << ", ";
  dbg(y...);
}
template <typename T>
void printv(vec<T> v, char c = ' ') {
  bool spc = false;
  for (auto i : v)
    if (spc)
      cout << c << i;
    else
      cout << i, spc = true;
  cout << '\n';
}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T>
void amax(T &a, T b) {
  if (a < b) a = b;
}
template <typename T>
void amin(T &a, T b) {
  if (a > b) a = b;
}
void pmod(ll &a, ll b) { a = (a + b) % MOD; }
void mmod(ll &a, ll b) { a = (a - b + MOD) % MOD; }
void tmod(ll &a, ll b) { a = (a * b) % MOD; }
void UNI(vec<int> &v) {
  sort(v.begin(), v.end());
  v.resize(unique(v.begin(), v.end()) - v.begin());
}
int getint() {
  int ret;
  cin >> ret;
  return ret;
}
ll POW(ll a, ll b) {
  ll res = 1;
  do {
    if (b % 2) tmod(res, a);
    tmod(a, a);
  } while (b >>= 1);
  return res;
}
ll getll() {
  ll ret;
  cin >> ret;
  return ret;
}
const int MXN = 1000000;
const int N = MXN + 10;
vec<int> v;
struct node {
  node *lch, *rch;
  ll w, tag;
  node() {
    lch = rch = nullptr;
    w = tag = 0;
  }
  void pull() { w = lch->w + rch->w; }
  void push(int h) {
    if (1 << h & tag) swap(lch, rch);
    lch->tag ^= tag;
    rch->tag ^= tag;
    tag = 0;
  }
  void build(int l, int r) {
    if (l == r) {
      w = v[l];
      return;
    }
    lch = new node();
    rch = new node();
    int mid = l + r >> 1;
    lch->build(l, mid);
    rch->build(mid + 1, r);
    pull();
  }
  void modify(int p, int lb, int rb, int v, int h) {
    if (lb == rb) {
      w = v;
      return;
    }
    push(h);
    int mid = lb + rb >> 1;
    if (p <= mid) lch->modify(p, lb, mid, v, h - 1);
    if (mid < p) rch->modify(p, mid + 1, rb, v, h - 1);
    pull();
  }
  void rev(int k) { tag ^= (1 << k + 1) - 1; }
  void swp(int k) { tag ^= (1 << k + 1); }
  ll query(int l, int r, int lb, int rb, int h) {
    if (l <= lb && rb <= r) return w;
    push(h);
    int mid = lb + rb >> 1;
    ll ret = 0;
    if (l <= mid) ret += lch->query(l, r, lb, mid, h - 1);
    if (mid < r) ret += rch->query(l, r, mid + 1, rb, h - 1);
    return ret;
  }
};
void solve() {
  int h, n, m;
  node *root = new node;
  cin >> h >> m;
  n = 1 << h;
  v.resize(n + 1);
  for (int i = 1; i <= (n); i++) cin >> v[i];
  root->build(1, n);
  int typ, a, b;
  while (m--) {
    cin >> typ;
    if (typ == 1) {
      cin >> a >> b;
      root->modify(a, 1, n, b, h);
    } else if (typ == 2) {
      cin >> a;
      root->rev(a);
    } else if (typ == 3) {
      cin >> a;
      root->swp(a);
    } else {
      cin >> a >> b;
      cout << root->query(a, b, 1, n, h) << '\n';
    }
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int T = 1;
  while (T--) {
    solve();
  }
}
