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;
int swp[19], a[524292];
long long tree[524292];
void build(int l, int r, int index) {
  if (l > r) return;
  if (l == r) {
    tree[index] = a[l];
    return;
  }
  build(l, ((l + r) >> 1), (index << 1));
  build(((l + r) >> 1) + 1, r, (index << 1 | 1));
  tree[index] = tree[(index << 1)] + tree[(index << 1 | 1)];
}
void update(int pt, int l, int r, int index, int dep, long long val) {
  if (pt < l || pt > r || l > r) return;
  if (l == r) {
    tree[index] = val;
    return;
  }
  int shift = (1 << (dep - 1)) * swp[dep - 1];
  if (shift == 0) {
    if (pt <= ((l + r) >> 1)) {
      update(pt, l, ((l + r) >> 1), (index << 1), dep - 1, val);
    } else {
      update(pt, ((l + r) >> 1) + 1, r, (index << 1 | 1), dep - 1, val);
    }
  } else {
    if (pt <= ((l + r) >> 1)) {
      update(pt, l, ((l + r) >> 1), (index << 1 | 1), dep - 1, val);
    } else {
      update(pt, ((l + r) >> 1) + 1, r, (index << 1), dep - 1, val);
    }
  }
  tree[index] = tree[(index << 1)] + tree[(index << 1 | 1)];
}
long long query(int start, int end, int l, int r, int index, int dep) {
  if (start > end || l > r || start > r || l > end) return 0;
  if (start <= l && r <= end) return tree[index];
  int shift = (1 << (dep - 1)) * swp[dep - 1];
  if (shift == 0) {
    return query(start, end, l, ((l + r) >> 1), (index << 1), dep - 1) +
           query(start, end, ((l + r) >> 1) + 1, r, (index << 1 | 1), dep - 1);
  } else {
    return query(start, end, ((l + r) >> 1) + 1, r, (index << 1), dep - 1) +
           query(start, end, l, ((l + r) >> 1), (index << 1 | 1), dep - 1);
  }
}
int main() {
  int n, i, q;
  scanf("%d%d", &n, &q);
  for (i = 1; i <= (1 << n); ++i) scanf("%d", &a[i]);
  build(1, 1 << n, 1);
  while (q-- > 0) {
    int op;
    scanf("%d", &op);
    if (op == 1) {
      int idx, v;
      scanf("%d%d", &idx, &v);
      update(idx, 1, 1 << n, 1, n, v);
    } else if (op == 2) {
      int v;
      scanf("%d", &v);
      for (i = 0; i < v; ++i) swp[i] ^= 1;
    } else if (op == 3) {
      int v;
      scanf("%d", &v);
      swp[v] ^= 1;
    } else {
      int l, r;
      scanf("%d%d", &l, &r);
      printf("%I64d\n", query(l, r, 1, 1 << n, 1, n));
    }
  }
  return 0;
}
