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 <class T>
bool ckmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool ckmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}
bool swapped[20];
template <class T>
struct node {
  T val;
  int level;
  node* left;
  node* right;
  node(int lev) {
    this->level = lev;
    this->left = nullptr;
    this->right = nullptr;
  }
  node* getLeft() {
    if (level == 0) return nullptr;
    if (swapped[level - 1]) return right;
    return left;
  }
  void setLeft(node* val) {
    if (swapped[level - 1])
      right = val;
    else
      left = val;
  }
  node* getRight() {
    if (level == 0) return nullptr;
    if (swapped[level - 1]) return left;
    return right;
  }
  void setRight(node* val) {
    if (swapped[level - 1])
      left = val;
    else
      right = val;
  }
};
template <class T, int SZ>
struct segtree {
  node<T>* root;
  segtree() {
    root = new node<T>(__builtin_ctz(SZ));
    root->val = 0;
  }
  void updN(node<T>* n, int pos, T val) {
    if (n->level == 0) {
      n->val = val;
      return;
    }
    int mid = 1 << (n->level - 1);
    if (pos >= mid) {
      if (n->getRight() == nullptr) {
        n->setRight(new node<T>(n->level - 1));
        n->getRight()->val = 0;
      }
      updN(n->getRight(), pos - mid, val);
    } else {
      if (n->getLeft() == nullptr) {
        n->setLeft(new node<T>(n->level - 1));
        n->getLeft()->val = 0;
      }
      updN(n->getLeft(), pos, val);
    }
    T lv = (n->getLeft() == nullptr) ? 0 : n->getLeft()->val;
    T rv = (n->getRight() == nullptr) ? 0 : n->getRight()->val;
    n->val = lv + rv;
  }
  void upd(int pos, T val) { updN(root, pos, val); }
  T queryN(node<T>* n, int i1, int i2) {
    if (i2 < 0 || i1 >= (1 << (n->level))) return 0;
    if (n->level == 0) return n->val;
    if (i1 <= 0 && (1 << (n->level)) - 1 <= i2) return n->val;
    T a = 0;
    int mid = 1 << (n->level - 1);
    if (n->getLeft() != nullptr) a += queryN(n->getLeft(), i1, i2);
    if (n->getRight() != nullptr)
      a += queryN(n->getRight(), i1 - mid, i2 - mid);
    return a;
  }
  T query(int i1, int i2) { return queryN(root, i1, i2); }
  void swapit(int k) { swapped[k] ^= 1; }
};
const int MAX_N = (1 << 18);
segtree<long long, MAX_N> st;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, q;
  cin >> n >> q;
  n = (1 << n);
  for (int i = 0; i < n; i++) {
    long long x;
    cin >> x;
    st.upd(i, x);
  }
  for (int i = 0; i < q; i++) {
    int type;
    cin >> type;
    if (type == 1) {
      int idx, val;
      cin >> idx >> val;
      idx--;
      st.upd(idx, val);
    } else if (type == 2) {
      int k;
      cin >> k;
      for (int j = 0; j < k; j++) st.swapit(j);
    } else if (type == 3) {
      int k;
      cin >> k;
      st.swapit(k);
    } else {
      int l, r;
      cin >> l >> r;
      l--;
      r--;
      cout << st.query(l, r) << "\n";
    }
  }
}
