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;
const long long inf = 1e18;
const int N = 2e6 + 1;
const long long mod = 1e9 + 7;
const int bits = 20;
const long double pi = 3.14159265358979323846;
const int p = 31;
long long tree[4 * N];
long long arr[N];
int flipped[20];
void build(int ss, int se, int si) {
  if (ss == se) {
    tree[si] = arr[ss];
    return;
  }
  int mid = (ss + se) / 2;
  build(ss, mid, 2 * si + 1);
  build(mid + 1, se, 2 * si + 2);
  tree[si] = tree[2 * si + 1] + tree[2 * si + 2];
}
long long query(int qs, int qe, int ss, int se, int si, int level) {
  if (qs > qe || qs > se || qe < ss) {
    return 0;
  }
  if (qs <= ss && qe >= se) {
    return tree[si];
  }
  int mid = (ss + se) / 2;
  if (flipped[level]) {
    return query(qs, qe, ss, mid, 2 * si + 2, level - 1) +
           query(qs, qe, mid + 1, se, 2 * si + 1, level - 1);
  } else {
    return query(qs, qe, ss, mid, 2 * si + 1, level - 1) +
           query(qs, qe, mid + 1, se, 2 * si + 2, level - 1);
  }
}
void update(int qi, int ss, int se, int si, long long v, int level) {
  if (qi > se || qi < ss) {
    return;
  }
  if (se == ss) {
    arr[ss] = v;
    tree[si] = v;
    return;
  }
  int mid = (ss + se) / 2;
  if (flipped[level]) {
    update(qi, ss, mid, 2 * si + 2, v, level - 1);
    update(qi, mid + 1, se, 2 * si + 1, v, level - 1);
  } else {
    update(qi, ss, mid, 2 * si + 1, v, level - 1);
    update(qi, mid + 1, se, 2 * si + 2, v, level - 1);
  }
  tree[si] = tree[2 * si + 1] + tree[2 * si + 2];
}
void solve() {
  int logn, q;
  cin >> logn >> q;
  int n = 1 << logn;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
  }
  build(0, n - 1, 0);
  int t, x, k, l, r;
  while (q--) {
    cin >> t;
    if (t == 1) {
      cin >> x >> k;
      update(x - 1, 0, n - 1, 0, k, logn);
    } else if (t == 2) {
      cin >> k;
      for (int i = 0; i <= k; i++) flipped[i] ^= 1;
    } else if (t == 3) {
      cin >> k;
      flipped[k + 1] ^= 1;
    } else if (t == 4) {
      cin >> l >> r;
      cout << query(l - 1, r - 1, 0, n - 1, 0, logn) << "\n";
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  std::cout << std::fixed << std::setprecision(20);
  ;
  int t = 1;
  while (t--) {
    solve();
  }
}
