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;
long long st[600000];
int revers[30], sp[30];
void modify(int level, int ind, int l, int r, int pos, int val, int swap) {
  if (l == r) {
    st[ind] = val;
    return;
  }
  int mid = (l + r) >> 1;
  swap ^= revers[level];
  if (pos <= mid)
    modify(level - 1, (ind << 1) ^ swap ^ sp[level], l, mid, pos, val, swap);
  else
    modify(level - 1, (ind << 1 | 1) ^ swap ^ sp[level], mid + 1, r, pos, val,
           swap);
  st[ind] = st[ind << 1] + st[ind << 1 | 1];
}
long long ask(int level, int ind, int l, int r, int ll, int rr, int swap) {
  if (ll <= l && r <= rr) {
    return st[ind];
  }
  long long ret = 0;
  int mid = (l + r) >> 1;
  swap ^= revers[level];
  if (ll <= mid)
    ret += ask(level - 1, (ind << 1) ^ swap ^ sp[level], l, mid, ll, rr, swap);
  if (mid < rr)
    ret += ask(level - 1, (ind << 1 | 1) ^ swap ^ sp[level], mid + 1, r, ll, rr,
               swap);
  return ret;
}
int n, q;
int main() {
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= (1 << n); ++i) {
    int x;
    scanf("%d", &x);
    modify(n, 1, 1, 1 << n, i, x, 0);
  }
  for (int i = 1, t; i <= q; ++i) {
    scanf("%d", &t);
    if (t == 1) {
      int x, k;
      scanf("%d%d", &x, &k);
      modify(n, 1, 1, 1 << n, x, k, 0);
    } else if (t == 2) {
      int k;
      scanf("%d", &k);
      revers[k] ^= 1;
    } else if (t == 3) {
      int k;
      scanf("%d", &k);
      sp[k + 1] ^= 1;
    } else if (t == 4) {
      int l, r;
      scanf("%d%d", &l, &r);
      cout << ask(n, 1, 1, 1 << n, l, r, 0) << '\n';
    }
  }
}
