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;
struct node {
  vector<int64_t> mask;
  int64_t height;
  node *left, *right;
  int64_t lidx, ridx;
  int64_t aggregate;
  node() { mask.resize(19, 0); }
  void push() {
    if (mask[height]) {
      std::swap(left, right);
      mask[height] = 0;
    }
    for (int64_t i = 0; i < height; i++) {
      if (left) left->mask[i] ^= mask[i];
      if (right) right->mask[i] ^= mask[i];
      mask[i] = 0;
    }
    if (left) {
      left->lidx = lidx;
      left->ridx = (ridx + lidx) / 2;
    }
    if (right) {
      right->lidx = (ridx + lidx) / 2 + 1;
      right->ridx = ridx;
    }
  }
  int64_t replace(int64_t id, int64_t val) {
    int64_t old_val = aggregate;
    push();
    if (id == lidx && id == ridx)
      aggregate = val;
    else if (id < lidx || id > ridx) {
      return 0;
    } else {
      aggregate += left->replace(id, val);
      aggregate += right->replace(id, val);
    }
    return aggregate - old_val;
  }
  void swap(int64_t k) { mask[k] ^= 1; }
  void reverse(int64_t k) {
    for (int64_t i = 0; i < k; i++) mask[i] ^= 1;
  }
  int64_t sum(int64_t l, int64_t r) {
    push();
    int64_t ret = 0;
    if (lidx > r || ridx < l) {
      return 0;
    } else if (l <= lidx && r >= ridx) {
      return aggregate;
    } else {
      if (left) ret += left->sum(l, r);
      if (right) ret += right->sum(l, r);
      return ret;
    }
  }
  node *construct(vector<int64_t> &values) {
    queue<node *> q;
    for (int64_t i = 0; i < values.size(); i++) {
      node *tmp = new node;
      tmp->height = 0;
      tmp->lidx = i;
      tmp->ridx = i;
      tmp->left = 0;
      tmp->right = 0;
      tmp->aggregate = values[i];
      q.push(tmp);
    }
    for (int64_t h = 1; 1 << h <= values.size(); h++) {
      int64_t lim = q.size() / 2;
      for (int64_t i = 0; i < lim; i++) {
        node *tmp = new node;
        tmp->height = h;
        tmp->left = q.front();
        q.pop();
        tmp->right = q.front();
        q.pop();
        tmp->lidx = tmp->left->lidx;
        tmp->ridx = tmp->right->ridx;
        tmp->aggregate = tmp->left->aggregate + tmp->right->aggregate;
        q.push(tmp);
      }
    }
    return q.front();
  }
};
int main() {
  int64_t n, q;
  cin >> n >> q;
  n = 1 << n;
  vector<int64_t> a(n);
  for (int64_t i = 0; i < n; i++) cin >> a[i];
  node t;
  t = *(t.construct(a));
  while (q--) {
    int64_t op, first, second;
    cin >> op;
    cin >> first;
    if (op == 1 || op == 4) cin >> second;
    if (op == 1)
      t.replace(first - 1, second);
    else if (op == 2)
      t.reverse(first + 1);
    else if (op == 3)
      t.swap(first + 1);
    else
      cout << t.sum(first - 1, second - 1) << '\n';
  }
}
