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;
template <typename T>
void out(T x) {
  cout << x << endl;
  exit(0);
}
using ll = long long;
const ll mod = 1e9 + 7;
const int maxn = 1e6 + 5;
int logn, q;
int n;
ll sum[maxn];
bool swapped[maxn];
void upd(int i, ll val) {
  for (int li = 0; li < logn; li++) {
    if (swapped[li]) {
      i ^= (1 << li);
    }
  }
  i += n;
  sum[i] = val;
  for (i >>= 1; i > 0; i >>= 1) {
    sum[i] = sum[i * 2] + sum[i * 2 + 1];
  }
}
ll qry(int r) {
  if (r == n) return sum[1];
  int i = 1;
  ll res = 0;
  for (int li = logn - 1; li >= 0; li--) {
    i *= 2;
    if (swapped[li]) {
      if (r >> li & 1) {
        res += sum[i + 1];
      } else {
        i++;
      }
    } else {
      if (r >> li & 1) {
        res += sum[i];
        i++;
      }
    }
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> logn >> q;
  n = 1 << logn;
  for (int i = 0; i < n; i++) {
    cin >> sum[i + n];
  }
  for (int i = n - 1; i > 0; i--) {
    sum[i] = sum[2 * i] + sum[2 * i + 1];
  }
  while (q--) {
    int tt;
    cin >> tt;
    if (tt == 1) {
      int x, k;
      cin >> x >> k;
      --x;
      upd(x, k);
    }
    if (tt == 2) {
      int k;
      cin >> k;
      for (int i = 0; i < k; i++) {
        swapped[i] = !swapped[i];
      }
    }
    if (tt == 3) {
      int k;
      cin >> k;
      swapped[k] = !swapped[k];
    }
    if (tt == 4) {
      int l, r;
      cin >> l >> r;
      cout << qry(r) - qry(l - 1) << "\n";
    }
  }
  return 0;
}
