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 int N = 262150;
int n, q, a[N], l, L[20], R[20], loc[20], rt;
int sw[N * 4], rev[N * 4], m;
struct T {
  int l, r;
  long long sum;
  bool rev;
} t[N * 4];
void inline pushup(int p) { t[p].sum = t[t[p].l].sum + t[t[p].r].sum; }
int inline getSwap(int x) {
  int res = 0;
  for (; x; x -= x & -x) res += sw[x];
  return res;
}
int inline getRev(int x) {
  int res = 0;
  for (; x; x -= x & -x) res += rev[x];
  return res;
}
void inline addSwap(int x, int k) {
  for (; x <= m; x += x & -x) sw[x] += k;
}
void inline addRev(int x, int k) {
  for (; x <= m; x += x & -x) rev[x] += k;
}
void inline pushdown(int p, int k) {
  if (getSwap(p) & 1) {
    swap(t[p].l, t[p].r);
    addSwap(p, -1);
    addSwap(p + 1, 1);
  }
  if (getRev(p) & 1) {
    swap(t[p].l, t[p].r);
    addRev(p, -1);
    addRev(p + 1, 1);
    addRev(t[p].l, 1);
    addRev(t[p].l + 1, -1);
    addRev(t[p].r, 1);
    addRev(t[p].r + 1, -1);
  }
}
void build(int &p, int l, int r, int c) {
  p = (++R[c]);
  if (l == r) {
    t[p].sum = a[r];
    return;
  }
  int mid = (l + r) >> 1;
  build(t[p].l, l, mid, c - 1);
  build(t[p].r, mid + 1, r, c - 1);
  pushup(p);
}
void change(int p, int l, int r, int c, int x, int k) {
  if (l == r) {
    t[p].sum = k;
    return;
  }
  pushdown(p, c);
  int mid = (l + r) >> 1;
  if (x <= mid)
    change(t[p].l, l, mid, c - 1, x, k);
  else
    change(t[p].r, mid + 1, r, c - 1, x, k);
  pushup(p);
}
long long query(int p, int l, int r, int c, int x, int y) {
  if (x <= l && r <= y) return t[p].sum;
  pushdown(p, c);
  int mid = (l + r) >> 1;
  long long res = 0;
  if (x <= mid) res += query(t[p].l, l, mid, c - 1, x, y);
  if (mid < y) res += query(t[p].r, mid + 1, r, c - 1, x, y);
  return res;
}
int main() {
  scanf("%d%d", &n, &q);
  l = n;
  n = 1 << n;
  for (int i = l - 1; i >= 0; i--) R[i] = R[i + 1] + (1 << (l - (i + 1)));
  for (int i = 0; i <= l; i++) L[i] = R[i] + 1;
  for (int i = 1; i <= n; i++) scanf("%d", a + i);
  build(rt, 1, n, l);
  m = R[0];
  while (q--) {
    int opt;
    scanf("%d", &opt);
    if (opt == 1) {
      int x, k;
      scanf("%d%d", &x, &k);
      change(1, 1, n, l, x, k);
    } else if (opt == 2) {
      int k;
      scanf("%d", &k);
      addRev(L[k], 1);
      addRev(R[k] + 1, -1);
    } else if (opt == 3) {
      int k;
      scanf("%d", &k);
      ++k;
      addSwap(L[k], 1);
      addSwap(R[k] + 1, -1);
    } else if (opt == 4) {
      int a, b;
      scanf("%d%d", &a, &b);
      printf("%lld\n", query(1, 1, n, l, a, b));
    }
  }
  return 0;
}
