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 int64 = long long;
void DBG() { cerr << "]" << '\n'; }
template <class H, class... T>
void DBG(H h, T... t) {
  cerr << h;
  if (sizeof...(t)) cerr << ", ";
  DBG(t...);
}
struct stree {
  vector<int64> v;
  vector<int> sw;
  stree(int n, int lg) : v(4 * n), sw(lg) {}
  void build(int x, int st, int nd, const vector<int> &a) {
    if (st == nd) {
      v[x] = a[st];
      return;
    }
    int mid = (st + nd) >> 1;
    build(2 * x, st, mid, a);
    build(2 * x + 1, mid + 1, nd, a);
    v[x] = v[2 * x] + v[2 * x + 1];
  }
  void upd(int x, int st, int nd, int p, int k, int lg) {
    if (st > p || nd < p) return;
    if (st == nd) {
      v[x] = k;
      return;
    }
    int mid = (st + nd) >> 1;
    int half = lg - 1;
    if (!sw[half]) {
      upd(2 * x, st, mid, p, k, half);
      upd(2 * x + 1, mid + 1, nd, p, k, half);
    } else {
      upd(2 * x + 1, st, mid, p, k, half);
      upd(2 * x, mid + 1, nd, p, k, half);
    }
    v[x] = v[2 * x] + v[2 * x + 1];
  }
  int64 query(int x, int st, int nd, int a, int b, int lg) {
    if (st > b || nd < a) return 0;
    if (st >= a && nd <= b) return v[x];
    int mid = (st + nd) >> 1;
    int half = lg - 1;
    if (!sw[half])
      return query(2 * x, st, mid, a, b, half) +
             query(2 * x + 1, mid + 1, nd, a, b, half);
    return query(2 * x + 1, st, mid, a, b, half) +
           query(2 * x, mid + 1, nd, a, b, half);
  }
};
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0);
  int n, q;
  cin >> n >> q;
  int m = 1 << n;
  vector<int> a(m);
  for (int i = 0; i < m; i++) cin >> a[i];
  stree st(m, n);
  st.build(1, 0, m - 1, a);
  while (q--) {
    int op;
    cin >> op;
    if (op == 1) {
      int x, k;
      cin >> x >> k;
      x--;
      st.upd(1, 0, m - 1, x, k, n);
    } else if (op == 4) {
      int l, r;
      cin >> l >> r;
      l--, r--;
      cout << st.query(1, 0, m - 1, l, r, n) << '\n';
    } else {
      int x;
      cin >> x;
      if (op == 2)
        for (int i = 0; i < x; i++) st.sw[i] ^= 1;
      else
        st.sw[x] ^= 1;
    }
  }
  return 0;
}
